Consistency and asymptotic normality of M-estimates of scatter on Grassmann manifolds

Abstract

This work proposes a study of M-estimates of scatter for matrix angular central Gaussian distributions on Grassmann manifold G(m,r) of all vector subspaces of dimension r of Rm. Such distributions are associated to random subspaces generated by r i.i.d. multivariate centred normal random vectors, and are of interest in Bayesian model selection for cointegration. We provide a careful study of the existence and the unicity of such M-estimators using geometrical arguments, and then study their consistency and asymptotic normality.