Estimation of a covariance matrix in multivariate skew-normal distribution

Abstract

This article addresses the problem of estimating a covariance matrix in a multivariate skew-normal distribution relative to two different losses. The estimation problem can be reduced to that of a scale matrix of a noncentral Wishart distribution. The noncentrality parameter matrix, which is a nuisance parameter, brings about non optimality of the best triangular invariant estimators which are minimax under normality. Some improving techniques under normality are proven to remain robust under the multivariate skew-normal distribution.

Keywords:

• Cholesky decomposition
• hypergeometric function of matrix argument
• inadmissibility
• noncentral Wishart distribution
• shrinkage estimator

AMS 2010 SUBJECT CLASSIFICATIONS:

• Primary 62F10
• secondary 62J07

Acknowledgments

The authors would like to thank an anonymous reviewer for providing a helpful comment. The research of the first author was supported in part by Grant-in-Aid for Scientific Research (15K00055 and 18K11201) from Japan Society for the Promotion of Science. The research of the second author was supported in part by Grant-in-Aid for Scientific Research (15H01943 and 26330036) from Japan Society for the Promotion of Science.