Intrinsic covariance matrix estimation for multivariate elliptical distributions

Abstract

The property of statistical models not depending on the coordinate systems or model parametrization is one main interest of intrinsic inference in statistics. The intrinsic covariance matrix estimation is addressed for multivariate elliptical distributions in this paper. An optimal intrinsic covariance estimator is derived in the sense of minimizing the mean square Rao distance, and proved to own intrinsic unbiasedness. Specifically, the intrinsically unbiased estimators for elliptical distributions and mixture elliptical distributions are developed.