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Studenten im Sommer auf dem Campus Nord, rote Zahnräder im Hintergrund © Roland Baege​/​TU Dortmund

Publications

2021

  • Baksalary, O.M., Trenkler, G.: On formulae for the Moore - Penrose inverse of a columnwise partitioned matrix. Applied Mathematics and Computation 403, 125913.
  • Baksalary, O.M., Trenkler, G.: A partial ordering approach to characterize properties of a pair of orthogonal projectors. Indian Journal of Pure and Applied Mathematics 52, 323 - 334.
  • Baksalary, O.M., Trenkler, G.: The Moore - Penrose inverse - a hundred years on a front- line of physics research. The European Physical Journal H 46, 9, A 57.

2020

  • Baksalary, O.M., Trenkler, G.: On most perfect magic squares of order four. Linear and Multilinear Algebra, 1411 - 1423.

2017

  • Baksalary, O.M., Trenkler, G.: Further Characterizations of Functions of a Pair of Orthogonal Projectors. Discussiones Mathematicae - Probability and Statistics 37, 65 - 78.

2015

  • Baksalary, O.M., Trenkler, G.: On a Craig - Sakamoto theorem for orthogonal projectors. Empirical Economic and Finanzial Research, Methods and Practice; Book Series: Advanced Studies in Theoretical and Applied Econometrics (J. Beran, Y. Feng, H. Hebbel, eds), Springer, Heidelberg, 48, 479 - 484.

2014

  • Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Applied Mathematics and Computation 236, 450 - 457.
  • Baksalary, O.M., Trenkler, G.: On Subspace Distances Determined by Frobenius Norm. Linear Algebra and its Application 448, 245 - 263.
  • Baksalary, O.M., Trenkler, G.: Problem 1331. Elements of Mathematics 69, 162.
  • Baksalary, O.M., Trenkler, G.: Numerical Range of a Skew - Symmetric Matrix. Image 52, 48.

2013

  • Trenkler G., Trenkler, D.: On melancholic magic squares. Discussiones Mathematicae - Probability and Statistics 33, 111 - 119.
  • Baksalary, O.M., Trenkler, G.: On a pair of vector spaces. Applied Mathematics and Computation 219, 9572 - 9580.
  • Baksalary, O.M., Trenkler, G.: On Column and Null Spaces of Functions of A Pair of Oblique Projectors. Linear and Multilinear Algebra 61, 1116 - 1129.
  • Baksalary, O.M., Trenkler, G.: On k - Potent Matrices. The Electronic Journal of Linear Algebra 26, 466 - 470.
  • Baksalary, O.M., Liski, E., Trenkler, G.: Let us do the twist again. Statistical Papers 54, 1109 - 1119.
  • Baksalary, O.M., Trenkler, G.: On the Entries of Orthogonal Projection Matrices. Combinatorial Matrix Theory and Generalized Inverses of Matrices, R. B. Bapat, S. J. Kirkland, K. M. Prasad, S. Puntanen eds, Springer, New Delhi, 101 - 118.
  • Baksalary, O.M., Trenkler, G.: On a Craig - Sakamoto Theorem for Orthogonal Projectors. Empirical Economic and Financial Research - Theory, Methods and Practice; Book Series: Advanced Studies in Theoretical and Applied Econometrics, J. Beran, Y. Feng, H. Hebbel eds, Springer, Heidelberg, 48, 479 - 484.
  • Baksalary, O.M., Trenkler, G.: Problem 1312, Elements of Mathematics 68, 39.
  • Baksalary, O.M., Trenkler, G.: Problem 50 - 2. Range Hermitianness of Certain Functions of Projectors. Image 50, 44.
  • Baksalary, O.M., Trenkler, G.: Solution 50 - 2. Range Hermitianness of Certain Functions of Projectors. Image 51, 43.
  • Baksalary, O.M., Trenkler, G.: Another Proof of the Two-sidedness of Matrix Inverses. Image 50, 2.

2012

  • Schmidt, K., Trenkler, D., Trenkler, G.: A simple parametrization of 3 x 3 magic squares. International Journal of Mathematical in Science and Technology 43, 128 - 133.
  • Baksalary, O.M., Trenkler, G.: Eigenvalues of Sums and Differences of Idempotent Matrices. American Mathematical Monthly 119, 162 - 163.
  • Baksalary, O.M., Trenkler, G.: Rank Formulae from the Perspective of Orthogonal Projectors. Linear and Multilinear Algebra 59, 607 - 625, 2011.
  • Trenkler, D., Trenkler, G.: The Numerical Range of the Luoshu is a Piece of Cake - Almost. The College Mathematics Journal 43, 371 - 376.
  • Baksalary, O.M., Trenkler, G.: Reverse Order Law for the Core Inverse. Problem 48 - 1, Image 48, 40.
  • Baksalary, O.M., Trenkler, G.: Eigenvalues of Sums and Differences of Idempotent Matrices. Solution to Problem 11466. the American Mathematical Monthly 119, 162 - 163.

2011

  • Baksalary, O.M., Trenkler, G.: On Generalized Rotation Matrices. International Scholarly Research Network. Applied Mathematics, Vol 2011.
  • Baksalary, O.M., Trenkler, G.: On the Matrix Difference I - A. Computers and Mathematics with Applications 62, 2279 - 2288.
  • Baksalary, O.M., Trenkler, G.: On the Projectors FFplus and FplusF. Applied Mathematics and Compution 271, 10213 - 10223.
  • Chu, K. L. , Drury, S. W., Styan, G. P. H., Trenkler, G.: Magic Moore - Penrose Inverses and Philatelic Magic Squares with Special Emphasis on the Daniels - Zlobec Magic Square. Croatian Operational Research Review 2, 4 - 13.
  • Trenkler, G.: Between OLSE and BLUE. Australian and New Zealand Journal of Statistics 53, 289 - 303.
  • Baksalary, O.M., Trenkler, G.: Solution to Problem 928. The College Mathematics Journal 42, 237 - 238 , unpublished, but acknowledged as solvers.
  • Baksalary, O.M., Trenkler, G.: Equality in the Frobenius Inequality. The Mathematical Gazette 95, no. 532, 133.
  • Baksalary, O.M., Trenkler, G.: Another Characterization of Normality. Image 47, 40 .
  • Baksalary, O.M., Trenkler, G.: Solution to Problem 45 - 1: Column Space Counterparts of the Known Conditions for Orthogonal Projectors. Image 46, 39 - 40 .
  • Baksalary, O.M., Trenkler, G.: Space Decomposition in Terms of Column and Null Spaces. Problem 46 - 1, Image 46, 48.
  • Baksalary, O.M., Trenkler, G.: On Disjoint Range Matrices. Linear Algebra and its Applications 435, 1222 - 1240.

2010

  • Baksalary, O.M., Trenkler, G.: Subsets and subspaces. Applied Mathematics and Computation 216, 484 - 491.
  • Baksalary, O.M., Bernstein, D.S., Trenkler, G.: On the equality between rank and trace of an idempotent matrix. Applied Mathematics and Computation 217, 4076 - 4080.
  • Baksalary, O.M., Trenkler, G.: Core Inverse of Matrices. Linear and Multilinear Algebra 58, 681 - 697.
  • Trenkler, G.: A Note on the Basic Lemma of the Linear Identification Problem. Journal of Quantitative Economics.
  • Baksalary, O.M., Trenkler, G.: Eigenspaces of the Proper Rotation Matrices. International Journal of Mathematical Education in Science and Technology 41, 827 - 829.
  • Baksalary, O.M., Trenkler, G.: Solution to Problem 44 - 1. Constrained characterization of Hermitianness. Image 45, 40.
  • Baksalary, O.M., Trenkler, G.: Solution to Problem 44 - 4. Square Nilpotent Matrix. Image 45.
  • Baksalary, O.M., Trenkler, G.: Column Space Counterparts of the Known Conditions for Orthogonal Projectors. Problem 45 - 1. image 45, 48.

2009

  • Baksalary, O.M., Trenkler, G.: Eigenvalues of functions of orthogonal projectors. Linear Algebra and its Applications 431, 2172-2186.
  • Liu, S., Trenkler, G., Yang, Z.: Further inequalities involving the Khatri-Rao product. Linear Algebra and its Applications 430, 2696-2704.
  • Baksalary, O.M., Trenkler, G.: Revisitation of the product of two orthogonal projectors. Linear Algebra and its Applications 430, 2813-2833.
  • Baksalary, O.M., Trenkler, G.: Column space equalities for orthogonal projectors. Applied Mathematics and Computation 212, 519-529.
  • Baksalary, O.M., Styan, G.P.H., Trenkler, G.: On a matrix decomposition of Hartwig and Spindelböck. Linear Algebra and its Applications 430, 2798-2812.
  • Baksalary, O.M., Trenkler, G.: Functions of orthogonal projectors involving the Moore-Penrose inverse. Computers and Mathematics with Applications 59, 764-778.
  • Baksalary, O.M. and Trenkler, G.: On a subspace metric based on matrix rank. Linear Algebra and its Applications 432 , 1475-1491.

2008

  • Trenkler, D., Trenkler, G.: On the product of rotations. International Journal of Mathematical Education in Science and Technology 39, 94-104.
  • Trenkler, G.: A remark on proofs of the vector triple product law. International Journal of Mathematical Education in Science and Technology 39, 423.
  • Trenkler, D., Trenkler, G.: Problem 4/SP08. Statistical Papers 49, 803.
  • Baksalary, O. M., Liu, S., Trenkler, G.: Further results on generalized and hypergeneralized projectors. Linear Algebra and Its Applications 429, 1038-1050.
  • Baksalary, O. M., Trenkler, G.: An alternative approach to characterize the commutativity of orthogonal projectors. Discussiones Mathematicae, Probability and Statistics 28, 113-137.
  • Trenkler, G.: The vector cross product and 4x4 skew-symmetric matrices. In: Advances in Linear Models and Related Areas. Essays in Honor of Helge Toutenburg. Edited by Shalabh, Heumann, C., Springer, Heidelberg, 94-104.
  • Liu, S., Trenkler, G.: Hadamard, Khatri-Rao, Kronecker and other matrix products. International Journal of Information and Systems Science 4 (1), 160-177.
  • Baksalary, O. M., Trenkler, G.: Characterization of EP, normal and Hermitian matrices. Linear and Multilinear Algebra 56 (3), 299-304.
  • Baksalary, O. M., Trenkler, G.: Problem 11379. American Mathematical Monthly 115, 664.

2007

  • Styan, G. P. H., Trenkler, G.: Image Philatelic Corner reprise, Image 38, 9-12.
  • Trenkler, D., Trenkler, G.: On singular 3x3 semi-diagonal Latin squares, The Mathematical Gazette 91, 126-128.
  • Trenkler, G.: Sample mean and sample variance. Their covariance and their (in) dependence. Letter to the Editor. The American Statistician 61, 373.
  • Styan, G. P. H., Trenkler, G.: A philatelic excursion with Jeff Hunter in probability and matrix theory. Journal of Applied Mathematics and Decision Sciences, Vol. 2007, 1-10.
  • Trenkler, D., Trenkler, G.: Problem 1243. elements of mathematics 62, 81.
  • Baksalary, O. M., Trenkler, G.: Solution to Problem 37-3. Image 39, 27.
  • Liu, S., Trenkler, G.: An inequality involving the Khatri-Rao sum of positive definite matrices. Problem 39-3. image 39, 32.
  • Liu, S., Trenkler, G.: On the range of A+A*. Problem 39-2. Image 39, 32.
  • Baksalary, O. M., Trenkler, G.: Solution to Problem 37-6. Image 39, 30-31.
  • Baksalary, O. M., Trenkler, G.: Solution to Problem 37-1. Image 39, 23-24.
  • Baksalary, O. M., Trenkler, G.: Solution to Problem 37-2. Image 39, 25-26.

2006

  • Trenkler, G., Troschke, S.-O.: A Comprehensive Collection of Rules for Set Calculus. (submitted)
  • Trenkler, G.: Solution to Problem 35-8: A characterization of a particular class of square complex matrices. Image 36, 33-34.
  • Trenkler, G.: Solution to Problem 35-9: A range equality for idempotent hermitian matrices. Image 36, 43.
  • Trenkler, G.: Necessary and sufficient condition for A+A* to be a nonnegative definite matrix. Problem 36-7. Image 36, 35.
  • Trenkler, G.: On oblique and orthogonal projectors. In: Proceedings of the International Statistics Workshop. Contributions to Probability and Statistics. Applications and Challenges. Edited by Brown, P., Liu, S. and Sharma, D., World Scientific, New Jersey, 178-191.
  • Trenkler, G.: On the approximate variance of a nonlinear function of random variables. In: Proceedings of the International Statistics Workshop. Contributions to Probability and Statistics. Applications and Challenges. Edited by Brown, P., Liu, S. and Sharma, D., World Scientific, New Jersey, 178-191.
  • Trenkler, G.: Solution to Problem 5/SP05. Statistical Papers 47, 485.
  • Trenkler, G.: Estimation of the Hadamard and cross products of two mean vectors in multivariate analysis. Problem 4/SP06. Statistical Papers 47, 481.
  • Trenkler, D., Trenkler, G.: Problem 11124. American Mathematical Monthly 113-5, 459.
  • Trenkler, G.: Problem 822. The College Mathematics Journal 37, 143.
  • Trenkler, G.: Solution to Problem 36-7. Image 37, 29.
  • Trenkler, G.: Solution to Problem 36-8. Image 37, 30-31.
  • Trenkler, G.: Characterization of EP-ness. Problem 37-6. Image 37, 31.
  • Baksalary, O. M., Trenkler, G.: Another property for the sum of a matrix A and its Moore-Penrose inverse A+. Problem 37-1. Image 37, 32.
  • Baksalary, O. M., Trenkler, G.: Rank of a generalized projector. Problem 37-2. Image 37, 32.
  • Baksalary, O. M., Trenkler, G.: Rank of a nonnegative definite matrix. Problem 37-3. Image 37, 32.

2005

  • Trenkler, G.: Characterization of a matrix by rank and trace. Problem 795. The College Mathematics Journal 36.
  • Trenkler, G.: Comment on Problem 779. The College Mathematics Journal 36, 244.
  • Trenkler, G.: Solution to Problem 33-1. Image 34, 26-27.
  • Trenkler, G.: Solution to Problem 33-3. Image 34, 32.
  • Trenkler, G.: Solution to Problem 33-4. Image 34, 33.
  • Trenkler, G., Werner, H.J.: Solution to Problem 33-5. Image 34, 34.
  • Trenkler, G.: Solution to 33-6.2: Projectors and similarity. Image 34, 36.
  • Trenkler, G.: Solution to Problem 33-8.3: Singular value decomposition of a skew-symmetric real matrix. Image 34, 38-39.
  • Puntanen, S., Trenkler, G.: A multivariate version of Samuelson's inequality. Linear Algebra and its Applications 410, 143-149.
  • Farebrother, R.W., Trenkler, G.: On generalized quadratic matrices. Linear Algebra and its Applications 410, 244-253.
  • Frauendorf, E., Neudecker, H., Trenkler, G.: Multivariate data, the arithmetic mean and exchangeability of transformation. Linear Algebra and its Applications 410, 87-95.
  • Trenkler, G.: A property of the sum of a matrix A and its Moore-Penrose inverse. Problem 34-8. Image 34, 39.
  • Trenkler, G.: Sum property for the Moore-Penrose inverse of EP matrices. Problem 34-9. Image 34, 39.
  • Trenkler, G.: On the product of orthogonal projectors. Problem 34-10. Image 34, 39.
  • Trenkler, G.: Solution to Problem 1700. Mathematics Magazine 78, 243 (unpublished).
  • Neudecker, H., Trenkler, G.: Estimation of the Kronecker and inner product of two mean vectors in multivariate analysis. Discussiones Mathematicae, Probability and Statistics 25, 207-215.
  • Trenkler, D., Trenkler, G.: The Sherman-Morrison formula and eigenvalues of a special bordered matrix. Acta Math. Univ. Comenianae 74, 255-258.
  • Trenkler, G.: Solution to Problem 34-8: A property for the sum of a matrix A and its Moore-Penrose inverse. Image 35, 40.
  • Trenkler, G.: Solution to Problem 34-9: A sum property for the Moore-Penrose inverse of EP-matrices. Image 35, 41.
  • Trenkler, G.: Solution to Problem 34-10: On the product of orthogonal projectors. Image 35, 42.
  • Trenkler, G.: A characterization of oblique projectors. Problem 35-7. Image 35, 43.
  • Trenkler, G.: A characterization of a particular class of square complex matrices. Problem 35-8. Image 35, 43.
  • Trenkler, G.: A range equality for idempotent Hermitian matrices. Problem 35-9. Image 35, 43.

2004

  • Trenkler, G.: Solution to Problem 32-6. Image 33, 28.
  • Trenkler, G.: Solution to Problem 32-7. Image 33, 32.
  • Trenkler, G.: Singular value decomposition of a skew-symmetric matrix. Problem 33-8. Image 33, 35.
  • Trenkler, G.: Property of the cross product. Problem 33-7. Image 33, 35.
  • Trenkler, G.: An Euclidian norm property inR3. Problem 33-4. Image 33, 36.
  • Trenkler, G.: Solution to Problem 32-5.1: Diagonal matrices solving a matrix equation. Image 33, 26.
  • Trenkler, G.: Factorization of a projector. Problem 33-5. Image 33, 36.
  • Trenkler, G.: Projectors and similarity. Problem 33-6. Image 33, 36.
  • Trenkler, G.: Characterization of idempotent matrices by rank and trace. Problem 88L. The Mathematical Gazette, Vol 88, 588.
  • Trenkler, G.: Solution to Problem 31-6.5. Image 32, 29.
  • Trenkler, G.: Solution to Problem 31-7.4. Image 32, 35.
  • Trenkler, D., Trenkler, G.: Invariance of the vector cross product. Problem 32-7. Image 32, 39.
  • Trenkler, G.: A vector cross product property inR3. Problem 32-6. Image 32, 39.
  • Trenkler, G.: Most-perfect pandiagonal magic squares and their Moore-Penrose inverse. International Journal of Mathematical Education Science and Technology 35, 697-701.
  • Trenkler, G.: Square root of three squared complex numbers. Problem 11075. The American Mathematical Monthly 111, 361.
  • Trenkler, G.: An extension of Lagrange's identity to matrices. International Journal of Mathematical Education in Science and Technology 35, 245-249.
  • Trenkler, G.: Matrices which take a given vector into a given vector - revisited. The American Mathematical Monthly 111, 50-52.

2003

  • Trenkler, G.: Problem 1198. Elements of Mathematics 58, 127-130.
  • Trenkler, G.: Solution to Problem 30-7.3. Image 31, 42.
  • Trenkler, G.: A full rank factorization of a skew-symmetric matrix. Problem 31-6. Image 31, 43.
  • Trenkler, G.: On the product of orthogonal projectors. Problem 31-7. Image 31, 43.
  • Groß, J., Trenkler, G.: A property of linear subspaces. Problem 31-1. Image 31, 44.
  • Trenkler, G.: Solution to Problem 30-6.2. Image 30, 39-40.
  • Trenkler, G.: Solution to Problem 30-4.3. Image 30, 36.
  • Neudecker, H., Trenkler, G., Zmyslony, R.: Estimation of the cross-product of two mean vectors. International Journal of Mathematical Education in Science and Technology 34, 928-935.
  • Trenkler, G.: Solution to Problem 02.6.1. oblique projectors. Econometric Theory 19, 1195-1196.
  • Trenkler, G.: A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Linear Algebra and its Applications 372, 207-224.
  • Trenkler, G.: A matrix equation over an arbitrary field. Problem 759. The College Mathematics Journal 34, 759.
  • Trenkler, G.: Trace and product of orthogonal projectors. Problem 11028. The American Mathematical Monthly 110, 636.
  • Trenkler, G.: A condition for an idempotent matrix to be hermitian. Problem 30-7. Image 30, 35.
  • Trenkler, G.: A matrix related to an idempotent matrix. Problem 30-6. Image 30, 35.
  • Trenkler, D., Trenkler, G.: Solution to Problem 29-12. Image 30.
  • Trenkler, G.: Solution to Problem 29-8. Image 30.
  • Trenkler, G.: Product of two complex orthogonal projectors. Problem 1661. Mathematics Magazine 75, 400.
  • Trenkler, D., Trenkler, G.: On the square root of aa' and bb'. The College Mathematics Journal 34, 39-41.
  • Trenkler, G.: Solution to Problem 02.1.2: A particular symmetric idempotent matrix. Econometric Theory 19, 228 (unpublished).

2002

  • Gnot, S., Stemann, D., Trenkler, G. and Urbanska-Motyka, A.: Maximum likelihood estimation in mixed normal models with two variance components. Statistics 36, 283-302.
  • Groß, J., Trenkler, G.: Complementing remarks on a matrix extension of a Cauchy-Schwarz inequality. Journal of Statistical Computation and Simulation 72, 26-29.
  • Gross, J., Trenkler, G.: Problem 10917. American Mathematical Monthly 109, 77.
  • Gross, J., Trenkler, G.: Product of two Hermitian nonnegative definite matrices. Problem 29-5. image 29, 36.
  • Neudecker, H., Trenkler, G.: Third and fourth moment matrices of vec X' in multivariate analysis. Linear Algebra and its Applications 354, 223-229.
  • Pordzik, P., Trenkler, G.: On efficiently estimable parametric functionals in the general linear model with nuisance parameters.Handbook of Applied Econometrics and Statistical Inference (ed. by A. Ullah, A.T.K. Wang and A. Chaturvedi), Marcel Dekker, New York, 45-52.
  • Trenkler, D., Trenkler, G.: Square roots and additivity. Problem 28-6. image 28, 35.
  • Trenkler, D., Trenkler, G.: Matrices commuting with the vector cross product. Problem 29-12. Image 29, 35.
  • Trenkler, G.: Solutions to Problem 27-2. Image 28, 30.
  • Trenkler, G.: Solution to Problem 1171. Elements of Mathematics 57, 133-134.
  • Trenkler, G.: Problem 1/SP02. Statistical Papers 43, 302.
  • Trenkler, G.: Oblique projectors. Problem 02.6.1. Econometric Theory 18, 1461.
  • Trenkler, G: The Moore-Penrose inverse and the vector product. International Journal of Mathematical Education in Science and Technology 33, 431-436.
  • Trenkler, G.: Solution to Problem 27-5. Image 28, 33.
  • Trenkler, G.: Partial isometry and idempotent matrices. Problem 28-7. Image 28, 35.

2001

  • Diersen, J., Trenkler, G.: Weighted records tests for splitted series of observation. Mathematical Statistics with Applications in Biometry. A Festschrift in Honour of Prof. Dr. Siegfried Schach [eds. Kunert, J., Trenkler, G.]. Josef Eul Verlag Köln, 163-178.
  • Gross, J.: Löwner partial ordering and space preordering of Hermitian nonnegative definite matrices. Linear Algebra and Its Applications, Vol. 326, 215-223.
  • Gross, J., Trenkler, G.: Specific generalized inverses. Problem 27-2. Image 27, 36.
  • Gross, J., Trenkler, G. and Troschke, S.-O.: Quaternions: Further contributions to a matrix oriented approach. Linear Algebra and Its Applications, Vol. 326, No. 1-3, 205-213.
  • Gross, J., Trenkler, G and Werner, H.J.: The equality between linear transforms of ordinary least squares and best linear unbiased estimator. Sankhya, Series A, Vol. 63, 118-127.
  • Schmidt, K. and Trenkler, G.: The Moore-Penrose inverse of a semi-magic square is semi-magic. International Journal of Mathematical Education in Science and Technology, Vol. 32, No. 4, 624-629.
  • Song, S.H., Trenkler, G.: On the efficiency of the Cochrane-Orcutt estimator in the serially correlated error components regression model for panel data. Communications in Statistics - Simulation and Computation, Vol. 30, 195-207.
  • Trenkler, D. and Trenkler, G.: Measure of overdispersion. Problem 2/SP01. Statistical Papers 42, 412.
  • Trenkler, D. and Trenkler, G.: Magic squares, melancholy and the Moore-Penrose inverse. Image 27, 3-10.
  • Trenkler, G.: A Comparison of the Ridge and the Iteration Estimator. Econometric Studies. A Festschrift in Honour of Joachim Frohn [eds. Friedmann, R., Knüppel, L. and Lütkepohl, H.]. Lit Verlag Munich, 73-87.
  • Trenkler, G.: A second-degree matrix equation - solution. Econometric Theory 17, 670.
  • Trenkler, G.: The simple third problem. Elements of Mathematics, Vol. 56, 130.
  • Trenkler, G.: Greatest lower bound. Problem 1622. Mathematics Magazine, 155.
  • Trenkler, G.: Problem 706: Trace-characterization of orthogonal projectors. The College Mathematics Journal 32, 297.
  • Trenkler, G.:The Vector Cross Product from an Algebraic Point of View. Discussiones Mathematicae - General Algebra and Applications 21, 67-82.
  • Trenkler, G.: Problem 368: Expectation and dispersion matrix of the vector cross product of two random vectors. Statistica Neerlandica 55, 382.
  • Trenkler, G.: Orthogonal projectors and the Löwner ordering. Problem 27-5. Image 27, 36.

2000

  • Gross, J.: The Moore-Penrose inverse of a partitioned nonnegative definite matrix. Linear Algebra and Its Applications, Vol. 321, No. 1-3, 113-121.
  • Gross, J.: Nonnegative and positive definite solutions to the matrix equation AXA*=B -- Revisited. Linear Algebra and Its Applications. Vol. 321, No. 1-3, 123-129.
  • Gross, J. and Puntanen, S.: A comment on pseudo-generalized least squares. Econometric Reviews, Vol. 19, No. 1, 131-133.
  • Gross, J. and Puntanen, S.: Estimation under a general partitioned linear model. Linear Algebra and Its Applications, Vol. 321, No. 1-3, 131-144.
  • Groß, J., Trenkler, G. and Troschke, S.O.: Moore-penrose inverse of a skew-symmetric matrix. Problem 25-1. image 25 , 16
  • Groß, J., Trenkler, G. and Troschke, S.O.: Quaternions. Further contributions to a matrix oriented approach. Linear Algebra and its Applications, 326, 205-213.
  • Groß, J., Trenkler, G., Werner, H.J.: The equality between linear transforms of ordinary least squares and best linear unbiased estimator. Sankhya, Series A, 63, 118-127.
  • Stemann, D. and Trenkler, G.: Some Further Results of the Cochrane-Orcutt Estimator. Journal of Statistical Planning and Inference 88, 205-214.
  • Trenkler, G.: On a generalization of the covariance matrix of the multinomial distribution. A Festschrift for Heinz Neudecker [eds. Heijmans, R.D.H., Pollock, D.S.G., Satorra, A.]. Kluwer Academic Publishers, Dordrecht, Boston, London, 67-73.
  • Trenkler, G.: Paradox is when a herring is lost. Working Paper No. 44, Department of Statistics, University of Dortmund.
  • Trenkler, G., Zmyslony, R.: Decomposition of symmetric matrices. Problem 24-9. Image 24, 17
  • Trenkler, G., Zmyslony, R.: Solution to Problem 24-9. Image 25, 15

1999

  • Gnot, S., Stemann, D., Trenkler, G. and Urbanska-Motyka, A.: On Maximum Likelihood Estimators in certain Multivariate Normal Mixed Models with two Variance Components. Tatra Mountains Mathematical Publications, Vol.17, 1-9.
  • Groß, J.: Solution to a rank equation. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 127-130.
  • Gross, J.: Explicit Solutions to the Matrix Inverse Problem AX=B. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 131-134.
  • Gross, J.: Idempotency of the Hermitian part of a complex matrix. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 135-139.
  • Gross, J.: On the product of orthogonal projectors. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 141-150.
  • Gross, J.: A note on the rank-subtractivity ordering. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 151-160.
  • Gross, J.: Local improvement of best linear unbiased estimation and admissibility under the weakly singular model. Communications in Statistics, Theory and Methods, Vol. 28, No. 8, 1803-1812.
  • Groß, J.: On oblique projection, rank additivity, and the Moore-Penrose inverse of the sum of two matrices. Linear and Multilinear Algebra, Vol. 46, 265-275.
  • Groß, J., Hauke, J. and Markiewicz, A.: Partial orderings, preorderings, and the polar decomposition of matrices. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 161-168.
  • Gross, J. and Markiewicz. A.: On admissibility of linear estimators with respect to the mean square error matrix criterion under the general mixed linear model. Statistics, Vol. 33, 57-71.
  • Groß, J. and Trenkler, G.: Nonsingularity of the difference of two oblique projectors. SIAM Journal on Matrix Analysis and Applications, Vol. 21, No. 2, 390-395.
  • Gross, J. and Trenkler, G.: Solution 22-3.5. image, The Bulletin of the International Linear Algebra Society, Issue 23, 23.
  • Gross, J., Trenkler, G. and Troschke, S.O.: On semi-orthogonality and a special class of matrices. Linear Algebra and Its Applications, Vol. 289, No. 1-3, 169-182.
  • Groß, J., Trenkler, G. and Troschke, S.O.: The vector cross product in C 3. International Journal of Mathematical Education in Science and Technology, Vol. 30, No. 4, 549-555.
  • Groß, J., Troschke, S.-O. and Trenkler, G.: On properties of 3 x 3 semi-magic squares. International Journal of Mathematical Education in Science and Technology, Vol. 30, No. 6, 861-865.
  • Trenkler, G.: On the eigenvalues of magic squares. International Journal of Mathematical Education in Science and Technology, Vol. 30, 307-308.
  • Trenkler, G.: A remark on prediction problems in regression analysis. Journal of Statistical Research, Vol. 33, No. 2.
  • Trenkler, G.: The simple third problem. Elements of Mathematics, Vol. 54, 38.
  • Trenkler, G.: Solution to Problem 21.4. Image, Vol. 22, 30.

1998

  • Gross, J.: More on concavity of a matrix function. SIAM Journal on Matrix Analysis and Applications, Vol. 19, No. 2, 365-368.
  • Gross, J.:. A note on the concepts of linear and quadratic sufficiency. Journal of Statistical Planning and Inference, Vol. 70, 69-76.
  • Gross, J.: Schur's inequality reconsidered. International Journal of Mathematical Education in Science and Technology, Vol. 29, No. 4, 629-630.
  • Gross, J.: A "classical inequality" for positive semidefinite matrices. International Journal of Mathematical Education in Science and Technology, Vol. 29, No. 5, 785-788.
  • Groß, J.: Statistical estimation by a linear combination of two given statistics. Statistics & Probability Letters, Vol. 39, No. 4, 379-384.
  • Gross, J.: On contractions in linear regression. Journal of Statistical Planning and Inference, Vol. 74, No. 2, 343-351.
  • Gross, J.: A note on the general Hermitian solution to AXA*=B. Bulletin of the Malaysian Mathematical Society, Vol. 21, 57-62.
  • Gross, J.:. Solution 20-6.1. image, The Bulletin of the International Linear Algebra Society, Issue 21, 27.
  • Gross, J. and Trenkler, G.: On the equality of linear statistics in the general Gauss-Markov model. In: Frontiers in Probability and Statistics (Mukherjee, S.P., Basu, S.K., Sinha, B.K. (Ed.)), Narosa Publishing House, New Delhi, 189-194.
  • Gross, J. and Trenkler, G.: On the product of oblique projectors. Linear and Multilinear Algebra, Vol. 44, No. 3, 247-260.
  • Groß, J., Trenkler, G. and Liski, E.: Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Journal of Statistical Planning and Inference, Vol. 71, 109-116.
  • Groß, J., Trenkler, G. and Troschke, S.O.: Characterization of complex matrices. Problem 10645. The American Mathematical Monthly, Vol. 105, 175.
  • Trenkler, G.: Four Square Roots of the Vector Cross Product. The Mathematical Gazette, Vol. 82, 100 - 102.
  • Trenkler, G.: Continuity of Transposition. Problem 20-4. Image, Vol. 20, 32.
  • Trenkler, G.: Another Look at Cubes and Inverses of Magic Squares. The Mathematical Gazette, Vol. 82, 288 - 289.
  • Trenkler, G.: On the exchangeability of transformations and the arithmetic mean. Journal of Statistical Computation and Simulation, 61, 305-307.
  • Trenkler, G.: Vector Equations and Their Solutions. International Journal of Mathematical Education in Science and Technology, Vol. 29, 455 - 459.
  • Trenkler, G.: Quasi-Idempotent Matrices. Problem 619. The College Mathematics Journal, Vol. 29, 66.
  • Trenkler, G.: Two results on the efficiency of the Almon lag technique. Journal of Quantitative Economics, Vol.14, 17-22.
  • Trenkler, G.: Square complex matrix, its Moore-Penrose inverse and the Löwner ordering.Problem 21.4, Image, Vol.21, 28.
  • Trenkler, G., Toutenburg, H.: Using first differences as a device against multicollinearity. In: R. Galata and H. Küchenhoff (eds.), Econometrics in Theory and Practice, Physica Verlag, Heidelberg, New York, 131-135.

1997

  • Groß, J.: Some remarks on partial orderings of hermitian matrices. Linear and Multilinear Algebra, Vol. 42, 53-60.
  • Gross, J.: Special generalized inverse matrices connected with the theory of unified least squares. Linear Algebra and Its Applications, Vol. 264, No. 1-3, 325-327.
  • Gross, J.: On semi-star related matrices. Linear Algebra and Its Applications, Vol. 264, No. 1-3, 495-503.
  • Gross, J.: A note on equality of MINQUE and simple estimator in the general Gauss-Markov model. Statistics & Probability Letters, Vol. 35, 335-339.
  • Gross, J.: A note on a partial ordering in the set of hermitian matrices. SIAM Journal on Matrix Analysis and Applications, Vol. 18, No. 4, 887-892.
  • Groß, J.: Some remarks concerning the reverse order law. Discussiones Mathematicae-Algebra and Stochastic Methods, Vol. 17, No. 2, 135-141.
  • Groß, J., Hauke, J. and Markiewicz, A.: Some comments on matrix partial orderings. Discussiones Mathematicae-Algebra and Stochastic Methods, Vol. 17, No. 2, 203-214.
  • Groß, J. and Trenkler, G.: Generalized and hypergeneralized projectors. Linear Algebra and Its Applications, Vol. 264, No. 1-3, 463-474.
  • Groß, J. and Trenkler, G.: Heteroscedastic fixed effects models. Solution to Problem 96.5.1. (Unpublished) Econometric Theory, 13, 891-893.
  • Groß, J. and Trenkler, G.: When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide?. Sankhya, Series A, Vol. 59, Part 2, 175-178.
  • Groß, J. and Trenkler, G.: On the equality of usual and Amemiya's partially generalized least squares estimator. Communications in Statistics, Theory and Methods, Vol. 26, No. 9, 2075-2086.
  • Groß, J. and Trenkler, G.: Restrictions and projections in linear regression. International Journal of Mathematical Education in Science and Technology, Vol. 28, No. 3, 465-468.
  • Gross, J. and Trenkler, G.: Solution 18-5.1. image, The Bulletin of the International Linear Algebra Society, Issue 19, 28.
  • Gross, J. and Trenkler, G.: Eigenvalues (problem). Image, The Bulletin of the International Linear Algebra Society, Issue 17, 32.
  • Gross, J. and Troschke, S.O.: Some remarks on partial orderings of non-negative definite matrices. Linear Algebra and Its Applications, Vol. 264, No. 1-3, 457-461.
  • Hartwig, R.E. and Trenkler, G.: Properties of Idempotent Matrix. Problem 97.3.3. econometric theory, Vol.13, 606.
  • Liski, E., Trenkler, G. and Groß, J.: Estimation from transformed data under the linear regression model. Statistics, Vol. 29, 205-219.
  • Tamaschke, S., Trenkler, G., Wei, L.: Mean square error matrix properties of bayes estimation for incorrect prior information under misspecification. Journal of the Italian Statistical Society, 6, 273-284.
  • Toutenburg, H. and Trenkler, G.: Using first differences as a device against multicollinearity. In: R. Galeta and H. Küchenhoff (eds.), Econometrics in Theory and Practice, Physica Verlag, Heidelberg, New York, 131-135.
  • Trenkler, G.: Hermitian Matrices. Solution to Problem 10377. The American Mathematical Monthly, 277 - 278.
  • Trenkler, G.: Two Imaginary Sisters of the Vector Cross-Product. Problem 18.6. Image, Vol.18, 32.
  • Trenkler, G.: Distribution of the Cross Product. Problem 338. Statistica Neerlandica, Vol. 51, 382.
  • Trenkler, G.: Generalization of a matrix inequality. Solution to Problem 96.2.3. (Unpublished) Econometric Theory, 13, 466.
  • Trenkler, G.: Roots of an orthogonal matrix. Solution to Problem 96.5.3. (Unpublished) Econometric Theory, 13, 894-896
  • Trenkler, G.: The symmetry of a Moore-Penrose inverse. Solution to Problem 96.4.5. (Unpublished) Econometric Theory, 13, 766-767
  • Trenkler, G. and Troschke, S.O.: On Matrices Whose Moore-Penrose Inverse is a Scalar Multiple of its Transpose. Problem 81.D. The Mathematical Gazette, Vol. 81, 128- 129.
  • Trenkler, G. and Troschke, S.O.: A system of power equations: Solution to Problem 581. (Unpublished) The College Mathematics Journal, 28, 317-318.
  • Trenkler, G. and Troschke, S.O.: Solution to Problem 81.D. The Mathematical Gazette, 81, 470-472
  • Trenkler, G., Troschke, S.O., Groß, J. and Puntanen, S.: Full commutativity under the trace for three matrices (problem). The College Mathematics Journal, Vol. 28, No. 4, 315.

1996

  • Diersen, J. and Trenkler, G.: Records Tests for Trend in Location. Statistics, Vol. 28, 1-12.
  • Gnot, S. and Trenkler, G.: Nonnegative Quadratic Estimation of the Mean Squared Errors of Minimax Estimators in the Linear Regression Model. Acta Applicandae Mathematicae, Vol. 43, 71 - 80.
  • Groß, J.: On a class of estimators in the general Gauss-Markov model. Communications in Statistics, Theory and Methods, Vol. 25, No. 2, 381-388.
  • Gross, J.: Estimation using the linear regression model with incomplete ellipsoidal restrictions. Acta Applicandae Mathematicae, Vol. 43, No. 1, 81-85.
  • Groß, J.: Comment on range invariance of matrix products. Linear and Multilinear Algebra, Vol. 41, No. 2, 157-160.
  • Gross, J.: Some remarks on the Löwner partial ordering of hermitian matrices. Discussiones Mathematicae-Algebra and Stochastic Methods, Vol. 16, No. 2, 191-195.
  • Groß, J.: When does A A* = B B*? (problem). Image, The Bulletin of the International Linear Algebra Society, Issue 17, p. 32.
  • Groß, J., Puntanen, S. and Trenkler, G.: On the equality of OLSE and BLUE in a partitioned linear model. In: The Proceedings of the A.C. Aitken Centenary Conference (Dunedin, 28 August - 1 September 1995), University of Otago, Bryan F.J. Manly, Ed., 143-152.
  • Gross, J. and Trenkler, G.: On the least squares distance between affine subspaces. Linear Algebra and Its Applications, Vol. 237/238, 269-276.
  • Groß, J. and Trenkler, G.: Prediction and the choice between two restricted regression models. Journal of Quantitative Economics, Vol. 12, No. 1, 125-131.
  • Gross, J. and Trenkler, G.: Orthogonal projectors. Problem 96.4.3. econometric theory, 12, 744.
  • Gross, J., Trenkler, G. and Troschke, S.O.: Characterization of Hermitian non-negative definite matrices (problem). Image, The Bulletin of the International Linear Algebra Society, Issue 17, 32.
  • Groß, J., Trenkler, G. and Troschke, S.O.: On a characterization associated with the matrix arithmetic and geometric means. Problem 17.2. image , 17, 32.
  • Groß, J., Trenkler, G. and Troschke, S.O.: A problem on idempotent matrices. Problem 10519 American Mathematical Monthly, 103, 347.
  • Gross, J., Trenkler, G. and Troschke, S.O.: Range hermitian projectors (problem). The American Mathematical Monthly, Vol. 103, No. 4, 347.
  • Ihorst, G. and Trenkler, G.: A General Investigation of the Mean Square Error Matrix Superiority in Linear Regression. Statistica, Vol.56, 15 - 25.
  • Pordzik, P. and Trenkler, G.: MSE Comparisons of Restricted Least Squares Estimators in Linear Regression Model - Revisited. Sankhya B, Vol. 58, 352 - 359.
  • Stahlecker, P., Knautz, H. and Trenkler, G.: Minimax Adjustment Technique in a Parameter Restricted Linear Model. Acta Applicandae Mathematicae, Vol. 43, 139 - 144.
  • Stahlecker, P., Knautz, H. and Trenkler, G.: Hypothesis Testing Using Affine Linear Estimators. Acta Applicandae Mathematicae, Vol. 43, 153 - 158.
  • Trenkler, G.: Why is econometrics needed? Prisma.Weekly magazine to the newspaper, No. 40, 44.
  • Trenkler, G.: Solution to: A Kronecker matrix inequality with a statistical application. Econometric Theory, 11, 654-655.
  • Trenkler, G. and Wei, L.: The Bayes estimator in a misspecified linear regression model. Test, vol. 5, 113-123.

1995

  • Gnot, S., Stemann, D., Trenkler, G.: Estimation of parameters in the linear regression model with equicorrelated errors. International Conference on Statistical Methods and Statistical Computing for Quality and Productivity Improvement. Proceedings Volume, 624-631, 1995
  • Gnot, S., Trenkler, G., Zmyslony, R.: Nonnegative minimum biased quadratic estimation in the linear regression model. Journal of Multivariate Analysis, 54, 113-125, 1995.
  • Groß, J., Trenkler, G. and Troschke, S.O.: A classification of square matrices. (Unpublished) 1995.
  • Ihorst, G., Trenkler, G.: Improved estimation by weak covariance adjustment technique. Discussiones Mathematicae, 15, 189-201, 1995.
  • Knautz, H., Trenkler, G.: Some bounds for bias and variance ofS2 under dependence. Scandinavian Journal of Statistics, 22, 121-128, 1995.
  • Trenkler, D., Trenkler, G.: The common mean, non-negative definite matrices, and APL. Vector, 12, 107-112, 1995
  • Trenkler, D., Trenkler, G.: An objective stability criterion for selecting the biasing parameter from the ridge trace. Industrial Mathematics, 45, 93-104, 1995
  • Trenkler, G.: A problem on tournament matrices. The Mathematical Gazette, 582, 1995
  • Trenkler, G.: A problem concerning generalized orthogonal projectors. Problem 1468. Mathematics Magazine, 582, 1995
  • Trenkler, G.: Solution to Problem 95.3.1: Optimal weighting of unbiased estimators. Econometric Theory, 12, 587-589, 1995
  • Trenkler, G.: Solution to Problem 95.3.3: An equivalence relation for two symmetric idempotent matrices. (Unpublished) Econometric Theory, 12, 590-592, 1995
  • Trenkler, G.: Solution to Problem 95.3.4: Aitken generalization of the Gauss-Markov theorem without calculus. (Unpublished) Econometric Theory, 12, 592-593, 1995
  • Trenkler, G.: Solution to Problem 95.3.5: Matrix results associated with Aitken's generalization of the Gauss-Markov theorem. (Unpublished) Econometric Theory, 12, 593-595, 1995
  • Trenkler, G.: On the singularity of the sample covariance matrix. Journal of Statistical Computation and Simulation, 52, 172-173, 1995
  • Trenkler, G.: Ordering of covariance matrices. Problem 95.4.2. Econometric Theory, 11, 796, 1995
  • Trenkler, G.: Moore-Penrose inverse of a matrix product with normal matrix. Econometric Theory, 11, 653-654, 1995
  • Trenkler, G.: Mean square error matrix superiority of empirical Bayes estimators under misspecification. Test, 4, 187-205, 1995
  • Trenkler, G., Troschke, S.O.: A new characterization of orthogonal projectors. Elements of Mathematics, 50, 171, 1995.
  • Trenkler, G., Wijekoon, P.: Pre-test estimation in the linear regressive model under stochastic restrictions. Ceylon Journal of Science: Physical Sciences, 2, 57-64, 1995.

1994

  • Trenkler, G.: Characterizations of oblique and orthogonal projectors. Proceedings of the International Conference on Linear Statistical Inference, LINSTAT '93, Eds. T. Calinski and R. Kala, Kluwer Academic Publishers, 255-270, 1994
  • Gnot, S., Knautz, H., Trenkler, G.: Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Proceedings of the International Conference on Linear Statistical Inference, LINSTAT '93, Eds. T. Calinski and R. Kala, Kluwer Academic Publishers, 65-71, 1994.
  • Gnot, S., Stemann, D., Trenkler, G.: Admissible nonnegative invariant quadratic estimation in linear models with two variance components. Proceedings of the International Conference on Linear Statistical Inference, LINSTAT '93, Eds. T. Calinski and R. Kala, Kluwer Academic Publishers, 129-137, 1994.
  • Pordzik, P., Trenkler, G.: Pre-test estimation in the linear regression model with competing restrictions. Linear Algebra and its Applications, 210, 123-137, 1994
  • Schipp, B., Stahlecker, P., Trenkler, G.: Assessing coverage-probabilities for approximate minimax estimators with respect to interval restrictions. Journal of Statistical Computation and Simulation, 50, 59-74, 1994
  • Stemann, D., Trenkler, G.: On the information loss of the Cochrane-Orcutt-estimation procedure. Journal of Quantitative Economics, 10, 227-234, 1994
  • Trenkler, G.: A matrix formulation on how deviant an observation can be. The American Statistician, 48, 60-61, 1994
  • Trenkler, G.: Solution to: A Cauchy-Schwarz inequality for determinants. (Unpublished) The American Mathematical Monthly, 101, 81-83, 1994
  • Trenkler, G.: On the Moore-Penrose inverse of a completely symmetric matrix. Journal of Statistical Computation and Simulation, 49, 230-231, 1994
  • Trenkler, G.: Singular magic squares. International Journal of Mathematical Education in Science and Technology, 25, 595-597, 1994

1993

  • Farebrother, R.W., Pordzik, P., Trenkler, G.: Characterization of an orthogonal projection matrix. Problem 93.3.5. econometric theory, 9, 523-524, 1993
  • Farebrother, R.W., Trenkler, G.: Characterization of a projector. Problem 93.4.6. econometric theory, 9, 690, 1993
  • Ihorst, G., Trenkler, G.: MSE-matrix superiority of the mixed over the least squares estimator in the presence of outliers. Communications in Statistics, A 22, 1865-1877, 1993.
  • Knautz, H., Trenkler, G.: On the correlation between X-bar andS2. Statistics & Probability Letters, 16, 235-237, 1993.
  • Knautz, H., Trenkler, G.: A note on the correlation betweenS2 and the least squares estimator in the linear regression model. Statistical Papers, 34, 237-246, 1993. Corrigendum: Statistical Papers, 35, 42, 1994.
  • Liski, E.P., Trenkler, G.: MSE-improvement of the least squares estimator by dropping variables. Metrika, 40, 263-269, 1993
  • Liski, E.P., Toutenburg, H., Trenkler, G.: Minimum mean square error estimation in linear regression. Journal of Statistical Planning and Inference, 37, 203-214, 1993.
  • Schipp, B., Trenkler, G.: Solution to: Generalized inverses of partitioned matrices. Econometric Theory, 9, 530-532, 1993
  • Stahlecker, P., Trenkler, G.: Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Journal of Statistical Planning and Inference, 36, 185-196, 1993.
  • Stahlecker, P., Trenkler, G.: Dropping variables versus use of proxy variables in linear regression. Journal of Statistical Planning and Inference, 50, 65-75, 1993.
  • Stahlecker, P., Trenkler, G.: Some further results on the use of proxy variables in prediction. The Review of Economics and Statistics, 75, 707-711, 1993.
  • Stemann, D., Trenkler, G.: Leverage and Cochrane-Orcutt estimation in linear regression. Communications in Statistics, A 22, 1315-1333, 1993.
  • Trenkler, G.: Solution to Problem 92.1.2. Econometric Theory, 9, 148, 1993.
  • Trenkler, G.: A note on comparing stochastically restricted estimators in a regression model. Biometrical Journal, 35, 125-128, 1993

1992

  • Baksalary, J.K., Schipp, B., Trenkler, G.: Some further results on hermitian matrix inequalities. Linear Algebra and its Applications, 160, 119-129, 1992.
  • Gnot, S., Knautz, H., Trenkler, G., Zmyslony, R.: Nonlinear unbiased estimation in linear models. Statistics, 23, 5-16, 1992.
  • Hessenius, H., Trenkler, G.: Pre-test estimation in the linear regression model with competing linear constraints. Statistica, 52, 17-31, 1992.
  • Knautz, H., Trenkler, G.: A note on the expected value of a Moore-Penrose inverse. International Journal of Mathematical Education in Science and Technology, 23, 155, 1992.
  • Liski, E.P., Toutenburg, H., Trenkler, G.: Optimal estimation methods under weakened linear restrictions in regression. Computational Statistics & Data Analysis, 14, 527-536, 1992.
  • Toutenburg, H., Trenkler, G.: Proxy variables and mean square error dominance in linear regression. Journal of Quantitative Economics, 8, 443-442, 1992.
  • Toutenburg, H., Trenkler, G.: Pretest procedures and forecasting in the regression model under restrictions. Journal of Statistical Planning and Inference, 30, 249-256, 1992.
  • Trenkler, G.: An elementary problem. The American Mathematical Monthly, 99, 571, 1992.
  • Trenkler, G.: On convexity of certain classes of estimators. Data Analysis and Statistical Inference, Festschrift in Honour of Friedhelm Eicker, Verlag Josef Eul, Bergisch Gladbach, Köln, 83-90, 1992
  • Trenkler, G.: Instrumental variables estimator and admissibility. Problem 92.1.2. Econometric Theory, 8, 145, 1992
  • Trenkler, G.: Solution to Problem 91.4.2. Econometric Theory, 8, 585-586, 1992

1991

  • Baksalary, J., Trenkler, G.: Covariance adjustment in biased estimation. Computational Statistics & Data Analysis, 12, 221-230, 1991.
  • Baksalary, J., Trenkler, G.: Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Linear Algebra and its Applications, 151, 169-184, 1991.
  • Gnot, S., Trenkler, G., Zmyslony, R.: Nonnegative estimation of the weighted squared length of the parameter vector in the linear regression model. (Unpublished), 1991.
  • Judge, G., Trenkler, G.: Estimation using proxy variables under squared error loss. (Unpublished), 1991.
  • Knautz, H., Trenkler, G.: Computation of expectation and variance for the binomial distribution. (in German) Praxis der Mathematik, 33, 24, 1991.
  • Knautz, H., Trenkler, G.: Dürer, Moore-Penrose, Drazin... (in German) Praxis der Mathematik, 33, 183-184, 1991.
  • Schipp, B., Trenkler, G.: A matrix equation. Econometric Theory, 7, 422-423, 1991.
  • Stahlecker, P., Trenkler, G.: Linear and ellipsoidal restrictions in linear regression. Statistics, 22, 163-176, 1991.
  • Trenkler, G.: Mean square error matrix comparisons between biased restricted least squares estimators. Sankhya, A53, 309-319, 1991.
  • Trenkler, G.: On the MSE-matrix comparisons of vector-valued estimators. Statistica Neerlandica, 45, 343, 1991.

1990

  • Baksalary, J., Pordzik, P., Trenkler, G.: A note on generalized ridge estimators. Communications in Statistics, A 19, 2871-2877, 1990.
  • Ihorst, G., Trenkler, G.: Matrix mean square error comparisons based on a certain covariance structure. Communications in Statistics, B 19, 1035-1043, 1990.
  • Michels, P., Trenkler, G.: Testing the stability of regression coefficients using recursive residuals. Australian Journal of Statistics, 32, 293-312, 1990.
  • Toutenburg, H., Trenkler, G.: Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Computational Statistics and Data Analysis, 10, 297-305, 1990.
  • Toutenburg, H., Trenkler, G.: Mean squared error matrix comparisons between biased estimators - An overview of recent results. Statistical Papers, 31, 165-179, 1990.

1989

  • Baksalary, J.K., Liski, E.P., Trenkler, G.: Mean squared error matrix improvements, mean squared error matrix improvements and admissibility of linear estimator. Journal of Statistical Planning and Inference, 23, 313-325, 1989.
  • Baksalary, J.K., Trenkler, G.: The efficiency of OLS in a seemingly unrelated regressions model - Solution and Comments. Econometric Theory, 463-465, 1989.
  • Baksalary, J.K., Trenkler, G.: Another view on least-squares estimation with a particular linear function of the dependent variable. (Unpublished), 1989.
  • Diersen, J., Trenkler, G.: Weighted records tests for splitted series of observations. (Unpublished), 1989.
  • Diersen, J., Trenkler, G.: Improving the efficiency of records tests for trend by splitting the series of observations. (Unpublished), 1989.
  • Toutenburg, H., Trenkler, G.: Mean square error matrix comparisons of forecasts in the linear regression model. Center for Multivariate Analysis, Penn State University, Technical Report No. 89 - 25, 1989.
  • Toutenburg, H., Trenkler, G.: Pre-test forecasts in the regression model based on linear restrictions. Research Paper No. 89/5, Department of Statistics, University of Dortmund, 1989.
  • Trenkler, G.: A curious result on least squares estimation in linear regression. International Journal of Mathematical Education in Science and Technology, 20, 475-476, 1989.
  • Trenkler, G.: A note on a superiority problem in misspecified restricted linear models. (Unpublished), 1989.
  • Trenkler, G., Wijekoon, P.: Mean square error matrix superiority of the mixed regression estimator under misspecification. Statistica, 49, 65-71, 1989.
  • Trenkler, G., Wijekoon, P.: Mean square error matrix superiority of estimators under linear restrictions and misspecification. Economics Letters, 30, 141-149, 1989.

1988

  • Liski, E.P., Trenkler, G.: Mean square error matrix dominance of estimators in the linear regression model with transformed data. Dept. of Math. Sciences, University of Tampere, Finland, Report A 196, 1988.
  • Stahlecker, P., Trenkler, G.: Full and partial minimax estimation in regression analysis with additional linear constraints. Linear Algebra and its Applications, 111, 279-292, 1988.
  • Trenkler, G.: Aphorisms on Statistics. (Unpublished), 1988.
  • Trenkler, G.: Some remarks on a ridge-type-estimator and good prior means. Communications in Statistics, A 17, 4251-4256, 1988.

1987

  • Büning, H., Naeve, P., Trenkler, G., Werner, H.J.: Mathematical concepts and principles for economic analysis. Oldenbourg Verlag, Munich, 1987
  • Hering, F., Schipp, B., Stahlecker, P., Trenkler, G.: Iterative improvements of a partial minimax estimator in regression analysis. Proc. Second International Tampere Conference in Statistics, 679-690, 1987.
  • Hering, F., Stahlecker, P., Trenkler, G.: Partial minimax estimation in regression analysis. Statistica Neerlandica, 41, 111-128, 1987.
  • Liski, E.P., Trenkler, G.: Some remarks on jack-knifing in ridge estimation. Department of Mathematical Sciences, University of Tampere, Finland, Report A195, 1987.
  • Schipp, B., Stahlecker, P., Trenkler, G.: Minimax estimation with additional linear restrictions: A simulation study. Communications in Statistics, B 17, 393-406, 1987.
  • Stahlecker, P., Trenkler, G.: Quasi minimax estimation in the linear regression model. Statistics, 18, 219-226, 1987.
  • Stahlecker, P., Trenkler, G.: Nonexpansive mappings, stability and epsilon-equilibria of multiple market models. (Unpublished), 1987.
  • Trenkler, G.: Mean square error matrix comparisons among restricted least squares estimators. Sankhya, A 49, 96-104, 1987.
  • Trenkler, G.: Another look at the matrix equation A x B = B. (Unpublished), 1987.

1986

  • Freund, E., Trenkler, G.: Mean square error matrix comparisons between mixed estimators. Statistica, 46, 493-501, 1986.
  • Liski, E.P., Trenkler, G.: Linear constraints and the efficiency of combined forecasts. Journal of Forecasting 5, no. 3, 197-202, 1986.
  • Liski, E.P., Trenkler, G.: Improved estimation by deleting variables in regression. (Unpublished), 1986
  • Trenkler, G.: Translation of: "Treatise on the upheaval of the moon around her axis and the apparent movement of the moon spots", from German into English, (Unpublished), 1986

1985

  • Schipp, B., Trenkler, D., Trenkler, G.: Updating the ridge estimator when additional explanatory variables or observations are available. Computational Statistics Quarterly, 2, 135-141, 1985.
  • Stahlecker, P., Trenkler, G.: On heterogeneous versions of the best linear and the ridge estimator. Proc. First Tampere Sem. Linear Models (1983), 301-322, 1985.
  • Trenkler, G.: Mean square error matrix comparisons of estimators in linear regression. Communications in Statistics, A 14, 2495-2509, 1985.
  • Trenkler, G.: Does weak consistency of an estimator imply asymptotic unbiasedness? Statistica Neerlandica, 39, 241-242, 1985.

1984

  • Jöhnk, M.-D., Trenkler, G.: Some remarks on the WiST case study: Straplag-AG, Part II. (Hannover, unpublished), 1984.
  • Trenkler, D., Trenkler, G.: Minimum mean square error ridge estimation. Sankhya, A 46, 94-101, 1984.
  • Trenkler, D., Trenkler, G.: On the euclidean distance between biased estimators. Communications in Statistics, A 13, 273-284, 1984.
  • Trenkler, D., Trenkler, G.: A simulation study comparing some biased estimators in the linear model. Computational Statistics Quarterly, 1, 45-60, 1984.
  • Trenkler, G.: Some further remarks on multicollinearity and the minimax conditions of the Bock-Stein-like estimator. Econometrica, 52, 1067-1069, 1984.
  • Trenkler, G.: On the performance of biased estimators in the linear regression model with correlated errors. Journal of Econometrics, 25, 179-190, 1984.

1983

  • Stahlecker, P., Trenkler, G.: Report on the selling behavior of department stores in Hannover. Report on behalf of the chamber of industry and commerce, Hannover, 1983.
  • Stahlecker, P., Trenkler, G.: A heterogeneous generalization of Theil's minimum mean square error estimator. Part I: Theoretical results. Discussion Paper, Department of Economics, University of Hannover, Ser. B, No. 11, 1983.
  • Stahlecker, P., Trenkler, G.: A heterogeneous generalization of Theil's minimum mean square error estimator. Part II: Simulation study results. Discussion Paper, Department of Economics, University of Hannover, Ser. B, No. 13, 1983.
  • Trenkler, D., Trenkler, G.: A note on superiority comparisons of homogeneous linear estimators. Communications in Statistics, A 12, 799-808, 1983.
  • Trenkler, G.: Mallows' Cp<//a> and optimal ridge constants. 7th Symposium on Operations Research St. Gallen; In: Methods of Operations Research, 44, (Eds. R. Henn, P. Kall et al.), Oelgeschlager, Gunn & Hain, Königstein and Cambridge, Mass. USA, 157-166, 1983.
  • Trenkler, G.: Biased linear estimators and estimable functions. Scandinavian Journal of Statistics, 10, 53-55, 1983.
  • Trenkler, G.: On the generalized variance of biased estimators in the linear model. Allgemeines Statistisches Archiv, 67, 199-201, 1983.
  • Trenkler, G.: Linear algebra for economics students, Department of Economics, University of Hannover, 1983.

1982

  • Borst, H.G., Daniel, W., Stegmann, T., Trenkler, G.: Therapeutic measures in experimental coronary air embolism. Langenbeck's Archives of Surgery, Stuttgart, 357, 213-214, 1982.
  • Trenkler, D., Trenkler, G.: Estimable functions and reduction of mean square error. In: Methods of Operations Research, 44, (Eds. R. Henn, P. Kall et al.), Oelgeschlager, Gunn & Hain, Königstein and Cambridge Mass., USA, 225-234, 1982.
  • Trenkler, G.: Partitions, sufficiency and undominated families of probability measures. Annals of the Institute of Statistical Mathematics, 34, 151-160, 1982.

1981

  • Borst, H.G., Oelert, H., Stegmann, T., Trenkler, G.: Total anomalous pulmonary venous connection: Surgical treatment in 35 infants. The Thoracic and Cardiovascular Surgeon, Stuttgart and New York, 29, 299-302, 1981.
  • Trenkler, D., Trenkler, G.: A comparison of the least-squares-estimator with biased alternatives. Operations Research Proceedings 1980, Springer-Verlag Berlin, Heidelberg, New York, 218-227, 1981.
  • Trenkler, G.: Biased estimators in the linear regression model. "Mathematical Systems in Economics" Vol. 58, Oelgeschlager, Gunn & Hain; Meisenheim and Cambridge Mass., USA, 1981
  • Trenkler, G.: Nonparametric tests in time series analysis, University of Hannover (Unpublished), 1981.
  • Trenkler, G.: On a generalized iteration estimator. In: Computational Statistics (Eds. H. Büning, P. Naeve), De Gruyter Verlag Berlin, New York, 315-335, 1981.

1980

  • Borst, H.G. et al, Oelert, H., Stegmann, T., Trenkler, G.: Experimental coronary air embolism. Assessment of time course of myocardial ischemia and the protective effect of cardiopulmonary bypass. The Thoracic and Cardiovascular Surgeon, Stuttgart and New York, 28, 141-149, 1980.
  • Trenkler, G.: Generalized mean squared error comparisons of biased regression estimators. Communications in Statistics, A 9, 1247-1259, 1980.
  • Trenkler, G.: New directions in econometrics and statistics. University of Hannover (Unpublished), 1980.

1979

  • Trenkler, G.: A new class of biased estimators in the linear model. Allgemeines Statistisches Archiv, 63, 76-77, 1979.

1978

  • Büning, H., Trenkler, G.: Nonparametric statistical methods. De Gruyter Verlag Berlin, New York, 1978, 2nd Edition 1994.
  • Krohn, U., Trenkler, G.: The iteration estimator: First empirical results. Discussion Paper, Faculty of Economics, University of Hannover. Ser. B, No. 3, 1978.
  • Trenkler, G.: An iteration estimator for the linear model. COMPSTAT 1978, Physica-Verlag, Vienna, 126-131, 1978.

1977

  • Trenkler, G.: An alternative to ridge- and shrunken-estimators in the linear regression model. Discussion Paper, Faculty of Economics, Technical University of Hannover. Ser. B, No. 1, 1977.

1976

  • Trenkler, G.: On a new method of testing statistical hypotheses. Annals of the Institute of Statistical Mathematics, A 28, No. 3, 371-384, 1976.

1973

  • Trenkler, G.: On a distance generating function of probability measures. Doctoral Dissertation, Free University of Berlin, 1973.

1971

  • Trenkler, G.: Basic statistics for students of economics, Free University of Berlin, University of Bielefeld and University of Hannover, Ch. 7 and 8, 1971 (2nd ed. 1980).

1969

  • Trenkler, G.: Nonarchimedian normed banach algebras, Master thesis, Free University of Berlin (Unpublished), 1969.
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