Robust methods for multivariate linear models with spectral models for scatter matrices

Abstract

The main goal of this dissertation is to present extensions to the robust estimation of multivariate location and scatter. These extensions include the estimation of structured scatter matrices embedded in a multivariate fixed effects model. Two different kinds of robust estimators are investigated. The first is based on Maronna's M-estimators of multivariate location and scatter (Maronna 1976). The second is a multivariate extension of the S-estimators introduced by Rousseeuw and Yohai (1984). In addition, asymptotic distributions of the estimators are derived from an estimating function approach. The sandwich estimator of the asymptotic variance is given, coupled with second order corrections to the bias of the estimators. Two different data sets are used to illustrate the techniques of the dissertation. A comparison of the new algorithms to Ruppert's SURREAL algorithm is made for each example. Models are fit to illustrate the flexibility of the new estimators. In addition, the sandwich estimate of the asymptotic variance is given for the examples. Simulations are performed evaluating the effectiveness of the estimators.