Robust Estimation of Dispersion Matrices and Principal Components

Abstract

Abstract This paper uses Monte Carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components. The estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and M-estimation. The M-estimators stand up exceptionally well. They and the multivariate trimming procedure are especially effective at estimating the principal components, including a near singularity. However, the M-estimators can break down relatively easily when the dimensionality is large and the outliers are asymmetric. With missing data, the element-wise approach becomes more attractive.