On Robust Estimation of Multivariate Location and Scale with Applications

Abstract

The principal objective of this thesis is, in a nutshell, to provide robust estimators of multivariate location and scale which have reasonable to high model efficiency but avoid high computational complexity so as to be practically useful in real problems. We utilize the minimum density power divergence (DPD) and the related philosophy to invoke robustness. There are some computational issues while minimizing the DPD in different multivariate set-ups. We will work on this problem rigorously and come up with three types of estimation procedures which are explicitly or implicitly related to the minimum DPD methodology, keeping the computational issue in mind each time. In particular, we develop a robust clustering algorithm based on mixture normal models in the first work where the component mean vectors and covariance matrices are estimated by minimizing the DPD with a suitable iteratively reweighted least squares (IRLS) algorithm. The second work proposes a sequential approach to minimize the DPD for location-scale estimation in case of elliptically symmetric probability models. The third work studies the one-step minimization of the DPD with various highly robust initializations and iterative procedures. We derive the theoretical properties (asymptotic and robustness features) of these methods, empirically validate them with extensive simulation studies in various set-ups and apply them in different problems in the domains of pattern recognition and machine learning.