Robust Methods for Functional Data Analysis

Abstract

Functional data consist of observed functions or curves at a finite subset of an interval. Each functional observation is a realization from a stochastic process. This thesis aims to develop suitable statistical methodologies for functional data analysis in the presence of outliers.

Statistical methodologies assume that functional data are homogeneous but in reality they contain functional outliers. Exploratory methods in functional data analysis are outlier sensitive. In this thesis we explore the effect of outliers in functional principal component analysis and propose a tool for identifying functional outliers by using robust functional principal components in a functional data. This is done by means of robust multivariate principal component analysis. Diagnostic plots based on functional principal component analysis are also found to be useful for identification and classification of functional outliers. Extensive simulation study is conducted to evaluate the performance of the proposed procedures and also real dataset is employed to illustrate the goodness of the method.

In addition, regression diagnostics for a functional regression model where regressors are functional data such as curves and the response is a scalar are discussed. We proposed a robust principal component based method for the estimation of the functional parameter in this type of functional regression model. Further we introduce robust diagnostic measures for identifying influential observations. A real dataset is also used to illustrate the usefulness of the proposed robust measures for detecting influential observations.