This paper considers the problem of estimating a covariance matrix under Stein’s loss. Sufficient conditions for the modified Efron–Morris estimator to be minimax under weighted quadratic loss are shown, which provide a general method for improving the estimator of the covariance matrix.

In this paper, we propose several new goodness-of-fit tests for normality based on the distance between the observed sample and the predictive sample drawn from the posterior predictive distribution. Note that the predictive sample is stochastic for a set of given sample observations, the...

We investigate the problem of estimating the Cholesky decomposition in a conditional independent normal model with missing data. Explicit expressions for the maximum likelihood estimators and unbiased estimators are derived. By introducing a special group, we obtain the best equivariant estimators.