The Department of Statistics and Econometrics works in the areas of linear model, matrix algebra, nonparametrics, point estimation, combining economic forecasts, admissibility, and on sports and statistics.
The so-called linear model is the most commonly used tool to represent reality in a statistically manageable form. This approach is used in almost all fields of application, especially in the field of economic research. The use of statistical methods to solve problems in the field of economics is summarized under the term econometrics.
In matrix algebra one deals with the various properties of matrices, which can also be understood as linear mappings from Rn to Rm. One tries to classify these mappings according to their properties, or investigates what happens if one connects several of these mappings. An important application of these investigations is the efficient solution of systems of equations.
In the context of ordinary statistics, including linear models, one is often forced to make certain assumptions about the distribution of random variables, often using the Gaussian normal distribution. In the context of nonparametric statistics, one derives methods that do without these additional assumptions. This is especially important if the distribution assumptions are not even approximately fulfilled. The procedures of non-parametrics still allow meaningful statements even in such cases.
In statistics, one is often confronted with the situation of wanting to estimate unknown parameters of a given distribution. For the univariate as well as for the multivariate case, a variety of estimation methods are available, which are based on different assumptions and approaches. These include maximum likelihood estimators, moment estimators, and jackknife estimators. Various characterization features, such as expectation fidelity, consistency or mean-square error, allow statements to be made about the quality of such point estimators.
Combination of economic forecasts
It is often the case that an important economic indicator such as gross national product is forecast by several economic research institutes. As a rule, these forecasts differ from one another to a greater or lesser extent, so that the question arises as to which of the forecasts should be trusted. Instead of deciding in favor of one of the forecasts, however, one can also try to combine the individual forecasts to form an overall forecast. Since each of the individual forecasts is based on partly different information, there is a legitimate hope that the combined forecast will be better than the individual forecasts.
If one uses certain decision rules (estimators) to solve statistical problems, it is reasonable to require that such rules are admissible within a class of decision rules. This is equivalent to saying that they cannot be uniformly outperformed by other rules from that class. In linear regression models, linear estimators of the parameter vector play an important role. Therefore, the investigation and description of admissible linear estimators is the subject of recent research. In addition, the question of the admissibility of nonlinear estimation procedures, such as Stein-type procedures, has also been investigated in the literature.
Sports and Statistics
Seminars on sports and statistics are held regularly at our department. Here, various sports (e.g. soccer, tennis, baseball, American soccer, basketball, figure skating, etc.) are analyzed from a statistical point of view. But also different competition systems are compared with each other or optimal strategies for the memory game are presented. Other topics include doping, home field advantage, and world record development in the 100-meter dash.