On the best equivariant estimator of covariance matrix of a multivariate normal population

Let X-1,...,X-n be independently and identically distributed normal m-vectors with mean mu and covariance matrix Sigma with mu'Sigma(-1) mu = C-2 where C > 0 is known. The best equivariant estimator of Sigma under loss functions L-1(Sigma,delta) = tr(Sigma(-1)delta - 1 gamma(Sigma(-1)delta-I) and L-2(Sigma,delta) = tr(Sigma(-1)delta) + log det(Sigma(-1)delta) - m is obtained respectively.Statistics & ProbabilitySCI(E)EI1ARTICLE82021-20342