Estimation of the precision matrix of a multivariate elliptically contoured stable distribution

Abstract

In this paper, we suggest two estimators of the precision matrix of the multivariate elliptically contoured stable distribution. The properties of these two estimators have been studied theoretically as well numerically. Conditions are given when one estimator dominates the other. Furthermore, trace of the precision matrix has been also estimated.

Keywords:

• matrix stable distribution
• estimation of the precision matrix
• quadratic loss
• decision theoretic estimation

AMS 2000 Subject Classification :

• Primary: 62H12
• Secondary: 62C15