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

TY - JOUR

T1 - Consistency and asymptotic normality of M-estimates of scatter on Grassmann manifolds

AU - Ciobotaru, Corina

AU - Mazza, Christian

PY - 2022/7

Y1 - 2022/7

N2 - 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.

AB - 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.

KW - Covariance matrix

KW - Grassmann manifold

KW - Matrix central angular distribution

UR - http://www.scopus.com/inward/record.url?scp=85127515524&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2022.104998

DO - 10.1016/j.jmva.2022.104998

M3 - Journal article

AN - SCOPUS:85127515524

SN - 0047-259X

VL - 190

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

M1 - 104998

ER -