Robustness of an Affine Equivariant Scatter Estimator Based on the Spatial Rank Covariance Matrix

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Kai Yu*+ and Xin Dang
• Companies: University of Mississippi and University of Mississippi
• Keywords: affine equivariant ; breakdown point ; influence function ; multivariate scatter ; spatial rank covariance matrix

Abstract

Visuri, Oja and Koivunen (2000) proposed a technique for robust covariance matrix estimation based on different notions of multivariate sign and rank. Among them, the spatial rank based covariance matrix estimator is especially appealing due to its high robustness, computational ease and good efficiency. Also, it is orthogonally equivariant under any distribution and affinely equivariant under elliptically symmetric distributions. In this talk, we study robustness properties of the estimator with respective to two measures: breakdown point and influence function. More specifically, the upper bound of the finite sample breakdown point can be achieved by a proper choice of univariate robust scale estimator. The influence functions for eigenvalues and eigenvectors of the estimator are derived, and they are found to be bounded under some assumptions. Finally, finite sample efficiency comparisons to popular robust MCD, M and S estimators are reported.