We propose an information criterion which measures the prediction risk of the predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive the criteria for selecting variables in linear regression models by putting the prior on the regression...

In this paper, we consider the problem of selecting explanatory variables of fixed effects in linear mixed models under covariate shift, which is the situation that the values of covariates in the predictive model are different from those in the observed model. We construct a variable selection...

　　 The paper develops empirical Bayes and benchmarked empirical Bayes estimators of positive small area means under multiplicative models. A simple example will be estimation of per capita income for small areas. It is now well-understood that small area estimation needs explicit,...

　　 In linear mixed models, the conditional Akaike Information Criterion (cAIC) is a procedure for variable selection in light of the prediction of specific clusters or random effects. This is useful in problems involving prediction of random effects such as small area estimation,...

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...

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...

One of the surprising decision-theoretic result Charles Stein discovered is the inadmissibility of the uniformly minimum variance unbiased estimator (UMVUE) of the variance of a normal distribution with an unknown mean. Some methods for deriving estimators better than the UMVUE were given by...