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Section C: Mathematical Statistics

Project C1: model choice and dynamic dependence structures

Project leaders

Holger Dette

Herold Dehling

Abstract

This project develops new statistical models and model selection procedures for the analysis of high-dimensional dynamic data structures. Important topics are model validation for functional data under complex and time-dependent dependence structures, new resampling methods for long-range dependence data, multivariate quantile regression, transitions from weak to strong dependence and the identification of stationary and non-stationary phases.

Project C2: Optimal Design of Experiments for Dynamic Processes

Project leaders

Holger Dette

Joachim Kunert

Abstract

The project proposes optimal designs for experiments in the context of dynamic models. It extends conventional theory for regression models with correlated observations to more general error processes, non-linear models and multivariate settings (time-space dependencies). Major topics are optimal design for the minimization of the mean square error, for model selection and for inverse problems. Another goal is the optimization of the design under model uncertainty, i.e. the construction of efficient designs for model selection, which require less a priori knowledge about the covariance structure and the specification of parameter values.

Project C3: Analysis of structural change in dynamic processes

Project leaders

Herold Dehling

Roland Fried

Abstract

This project considers structural changes in statistical models for time series and regression analysis. It improves upon existing methods for the detection of abrupt changes in levels, trend, and in the correlation structure under weak assumptions. In particular, it allows for heavy tails, heteroscedasticity and long memory, and develops procedures for change-point detection which work reliably under rather general conditions.

Project C5: Statistical inference for complex dynamical models in Empirical finance

Project leaders

Denis Belomestny

Jeannette Woerner

Abstract

This project develops novel procedures for generalized moving average processes and generalized diffusions of McKean-Vlasov- and Dunkl type. It focuses on instationary and non-linear processes and allows for a complex dependence structure in space and time including long range dependence. Among its goals are parametric and non-parametic estimating procedures for both low and high frequency data which combine methods from stochastic and time series analysis and generalized Fourier techniques.