Contributions to Functional Data Analysis With a Focus on Points of Impact in Functional Regression

Abstract

The focus of this thesis is on the estimation of an unknown number of unknown specific locations (points of impact) at which a functional predictor has a specific effect on a real valued dependent variable.<br /> Two general setups are considered: chapter 1 is concerend with estimating points of impact in a functional linear regression model, chapter 2 is concerned with estimating points of impact in a generalized functional linear regression model framework. Besides consistency results for the introduced estimator of the points of impact and their number, both chapters contain results for the estimation of the remaining model parameters.<br /> The last chapter is concerned with the analysis of juggling cycles. A registration procedure is followed by a functional principal component analysis and the analysis of the corresponding eigenfunctions and scores.