Research
Our research areas
- bootstrap
- change points
- copula estimation
- empirical processes
- testing model assumptions
- curve estimation
- regression
- residual processes
- time series analysis
Projects
Efficient nonparametric regression when the support is bounded (2013-2020)
– Project of the Research Unit 1735: “Structural Inference in Statistics: Adaptation and Efficiency” –
We consider nonparametric regression models where the support of the errors is bounded from at least one side, so that the regression function can be determined from the boundary of the support of the observations. Models of this type arise naturally, e.g., in the analysis of auctions, when dealing with bid and ask data from stock exchange, in the domain of production frontiers or image analysis. Particular emphasis is put on the nonregular case in which the error distribution concentrates sufficient mass in the neighbourhood of its endpoint(s).
In contrast to classical nonparametric mean regression estimators, which are based on local averages of the response random variables, boundary regression estimators depend on extreme observations. In cases where both estimating approaches are directly comparable (e.g., for symmetric error distributions with bounded support), the latter converge at a much faster rate if the error distribution is nonregular.
Unlike the structure of regular mean regression models, which has been thoroughly studied, nonparametric boundary regression experiments are less well understood, in particular if the regression function is assumed smooth, but not necessarily monotone or convex. We will approximate such experiments in which both the boundary function and the behaviour of the error distribution locally at the boundary of its support are unknown by simpler experiments. This way we will be able to construct optimal estimators and testing procedures which adapt to the unknown regularity of the boundary function and of the error distribution. Adaptive confidence bands for the regression function as well as hypotheses tests for assumptions on the error distribution and the structure of the regression function will be developed. Jointly with Project 5 (estimation of high-dimensional matrices) the new methods will be applied to estimate the realised volatility from observations of bid and ask prices.
The principal investigators are
Scientific staff is Leonie Selk.
Project website: Efficient nonparametric regression when the support is bounded
Semiparametric structural analysis in regression estimation (2017–2020)
– Project of the Research Unit 1735: “Structural Inference in Statistics: Adaptation and Efficiency” –
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.
The principal investigators are
Scientific staff is Leonie Selk.
Project website: Semiparametric structural analysis in regression estimation