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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Research Unit 1735

Semiparametric structural analysis in regression estimation

A structural analysis of regression data is a challenging task. Typically one aims at recovering the important structural features of an unknown curve without specifying its complete structure. 
A particular example is the problem of detecting structural breaks like jumps or  kinks of a piecewise smooth curve without any prior information on the amount and size of breaks. Another desirable feature of the analysis is stability and robustness against noise misspecification and noise inhomogeneity. The aim of the project is to develop novel methods of structural regression analysis based on multi-scale comparison and resampling techniques. The obtained results have to address the questions of optimality and efficiency of the proposed methods in the modern finite sample framework developed within the project. An important issue is the flexibility and applicability of the proposed techniques to different classes of regression models: it has to include the cases of complicated categorical data, inhomogeneous or dependent error distributions, mean and quantile regression, etc. The methods and the results will be extended to the case of unknown transformation in a regression model. We plan to comprehensively investigate estimation and testing theory for different semiparametric transformation regression models with nonparametric regression components. Jointly with Project 3 we will consider models with one-sided error distributions.

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