Robustifying principal component analysis with spatial sign vectors
Taskinen, S., Koch, I., & Oja, H. (2012). Robustifying principal component analysis with spatial sign vectors. Statistics and Probability Letters, 82 (4), 765-774. doi:10.1016/j.spl.2012.01.001
Published inStatistics and Probability Letters
© Elsevier. This is a pre-print version of an article whose final and definitive form has been published by Elsevier.
In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods.