This paper addresses the problem of estimating the mean vector of a singular multivariate normal distribution with an unknown singular covariance matrix. The maximum likelihood estimator is shown to be minimax relative to a quadratic loss weighted by the Moore-Penrose inverse of...

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 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....

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 the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It...

It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative values with positive probability. In this paper, improved truncated estimators of the risk, risk...

In this paper, we consider the problem of estimating the covariance matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available...

In this paper we consider the problem of estimating the regression parameters in a multiple linear regression model when the multicollinearity is present.Under the assumption of normality, we present three empirical Bayes estimators. One of them shrinks the least squares (LS) estimator towards...