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...

For Wishart density functions, the risk dominance problems of moment estimators, maximum likelihood estimators (MLEs), James-Stein type minimax estimators and their improved estimators of covariance matrices under the Kullback-Leibler loss function have been well studied in the literature....

Consider the problem of testing the linear hypothesis on the regression coefficients in the Fay-Herriot model which has been used in the small area problem. Since this model involves the random effects, a test based on the generalized least squares estimator, called the GLS test, depends on the...

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...

In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a...

In this article, Stein-Haff identity is established for a singular Wishart distribution with a positive definite mean matrix but with the dimension larger than the degrees of freedom. This identity is then used to obtain estimators of the precision matrix improving on the estimator based on 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...

In the simultaneous estimation of a mean of a multivariate normal distribution, Charles Stein discovered the surprising decision-theoretic result that the usual maximum likelihood estimator is inadmissible with respect to quadratic loss in three or more dimensions. Since then, the researches on...