On improved matrix estimators in high-dimensional data

Music City Center 

In this talk, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal
distribution with an unknown variance-covariance matrix. In particular, some recent results of are established in their full generalities and we revise some results which are useful in studying the risk dominance of shrinkage estimators. We generalize the existing methods in three ways. First, we consider a parametric estimation problem which is enclosed as a special case the one about the vector parameter. Second, we propose a class of James-Stein matrix estimators and, we establish a necessary and a sufficient condition for any member of the proposed class to have a finite risk function. Third, we present the conditions for the proposed class of estimators to dominate the maximum likelihood estimator. On the top of these interesting contributions, the additional novelty consists in the fact that, we extend the methods suitable for the vector parameter case and the derived results hold in the classical case as well as in the context of high and ultra-high dimensional data.

Invariant quadratic loss

James-Stein estimation

Location parameter

Minimax estimation

Moore-Penrose inverse

Risk function 

IMS