Robust covariance matrix estimation and multivariate outlier detection

Abstract

A severe limitation for the application of robust position and scale estimators having a high breakdown point is a consequence of their high computational cost. In this paper we present and analyze several inexpensive robust estimators for the co variance matrix, based on information obtained from projections onto certain sets of directions. The properties of these estimators (breakdown point, computational cost, bias) are analyzed and compared with those of the Stahel-Donoho estimator, through simulation studies. These studies show a clear improvement both on the computational requirements and the bias properties of the Stahel-Donoho estimator. The same ideas are also applied to the construction of procedures to detect outliers in multivariate samples. Their performance is analyzed by applying them to a set of test cases.