Estimation of a covariance matrix in multivariate skew-normal distribution

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.