While developing a prior distribution for any Bayesian analysis, it is important to check whether the corresponding posterior distribution becomes degenerate in the limit to the true parameter value as the sample size increases. In the same vein, it is also important to understand a more...

Let X1,..., Xp be p (= 3) independent random variables, where each Xi has a distribution belonging to the one-parameter exponential family of distributions. The problem is to estimate the unknown parameters simultaneously in the presence of extreme observations. C. Stein (Ann. Statist. 9 (1981),...

The paper considers estimation of matrix normal means. A class of empirical Bayes estimators is proposed which dominates the maximum likelihood estimator simultaneously for many quadratic losses. Several of these empirical Bayes estimators are compared in terms of their simulated risks, and a...

For the p-variate Poisson mean, under the sum of weighted squared error losses, weights being reciprocals of variances, a class of proper Bayes minimax estimates dominating the usual estimate, namely the sample mean is produced. An example is given to illustrate this. The interrelation of our...

A unified theory of simultaneous estimation of parameters for the continuous exponential family is presented. Estimators are constructed that improve on the standard ones (the maximum likelihood, UMVUE or best invariant estimator). These improved estimators shift the standard ones towards...

The paper develops a general class of shrinkage estimators for estimating the normal mean, which dominates the sample mean in three or higher dimensions under a general divergence loss. In the process, the earlier works of James and Stein [11] and Efron and Morris [5] are generalized...

Based on the notion of predictive influence functions, the paper develops multivariate limited translation hierarchical Bayes estimators of the normal mean vector which serve as a compromise between the hierarchical Bayes and maximum likelihood estimators. The paper demonstrates the superiority...

Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate...

For a multivariate normal distribution with unknown mean vector and unknown dispersion matrix, a sequential procedure for estimating the unknown mean vector is suggested. The procedure is shown to be asymptotically "risk efficient" in the sense of Starr (Ann. Math. Statist. (1966), 1173-1185),...

The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal...