Robust Projection Pursuit Estimator for Dispersion Matrices and Principal Components

摘要

This paper proposes and discusses the ROBUST PROJECTION PURSUIT ESTIMATOR for dispersion matrices and their principal components. This estimator finds robust principal components by searching, successively, for directions which maximize (minimize) a robust estimate of scale; the estimate of the dispersion matrix is constructed from the estimated principal components. These estimators are shown below (under mild conditions) to have a number of desirable properties. They are orthogonally equivariant and, within any elliptic underlying density family, asymptotically affinely equivariant. Furthermore, at elliptic densities, they are consistent and weakly continuous (i.e., qualitatively robust). Finally, they have good quantitative robustness - their breakdown point can be as high as 1/2. The robust projection pursuit approach is a promising alternatives to other estimators of dispersion matrices. (Author)