Robust functional principal component regression

Abstract

This diploma thesis is about robust functional principal component regression. It is based on functional data where we observe underlying stochastic processes. In a regression setting we want to regress a scalar response onto such stochastic process. As in a multivariate setting this regression is sensitive to outliers in both response and explaining variable. That means we want to robustify this regression. A common technique for such model is to use functional principal components of the corresponding process. In this thesis we give a short overview of functional data analysis including functional principal componentsas well as a brief introduction to robust statistics. We compare two different types of estimators. One is made for regular, densely observed data whereas a new approach for irregular, longitudinal data is proposed. In a simulation study all estimators are applied to 2 models in various settings. These cover regular and irregular as well as dense or sparse data. The data is used in both clean and contaminated fashion. The results of this simulation study are partly satisfying, especially in regular settings. However, in very sparse, irregular settings the estimators are not as good. Finally, the estimators are applied to a real world example. In the Canadian Weather data we regress the annual precipitationonto temperature curves in various locations. All methods perform comparably while the newly proposed methods seem to work the best.