In estimation of the normal covariance matrix, nding a least favorable sequence of prior distributions has been an open question for a long time. In this paper, we address the classical problem and succeed in construction of such a sequence, which establishes minimaxity of the best equivariant...

The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. Although a standard loss function is the Stein loss, it is not available in the case of a high dimension. In this paper, a new type of a quadratic loss function,...

　　 This paper addresses the problem of estimating the normal mean matrix with an unknown covariance matrix. Motivated by an empirical Bayes method, we suggest a unied form of the Efron-Morris type estimators based on the Moore-Penrose inverse. This form not only can be dened for...

This paper treats the problem of simultaneously estimating the precision matrices in multivariate normal distributions. A condition for improvement on the unbiased estimators of the precision matrices is derived under a quadratic loss function. The improvement condition is similar to the...

This paper addresses the Stein conjecture in the simultaneous estimation of a matrix mean of a multivariate normal distribution with a known covariance matrix. Stein (1973) derived an unbiased estimator of a risk function for orthogonally equivariant estimators and considered to isotonize the...

This paper treats the problem of estimating positive parameters restricted to a polyhedral convex cone which includes typical order restrictions such as simple order, tree order and umbrella order restrictions. In this paper, two methods are used to show the improvement of order-preserving...

This paper treats the problem of estimating the restricted means of normal distributions with a known variance, where the means are restricted to a polyhedral convex cone which includes various restrictions such as positive orthant, simple order, tree order and umbrella order restrictions. In...

This paper is concerned with the problem of estimating a matrix of means in multivariate normal distributions with an unknown covariance matrix under the quadratic loss function. It is first shown that the modified Efron-Morris estimator is characterized as certain empirical Bayes estimator....

This paper is concerned with the simultaneous estimation of parameters of regression coefficients and error variance in a linear regression model. Motivated from the Akaike information criterion, the expected Kullback-Leibler distance is employed as a risk function for comparing estimators in a...

In this paper, the simultaneous estimation of the precision parameters of k normal distributions is considered under the squared loss function in a decision-theoretic framework. Several classes of minimax estimators are derived by using the chi-square identity, and the generalized Bayes minimax...