The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. A bench-mark estimator of the linear combination is an unbiased estimator, which is minimax, but inadmissible relative to the mean squared error. An interesting...

　　 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,...

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 the small area estimation, the empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful because it gives a stable and reliable estimate for a mean of a small area. In practical situations where EBLUP is applied to...

Sample survey data can be used to derive a reliable estimate of a total mean for a large area. When the same data are used to estimate means of small areas like city, county or town belonging to the large area, the usual direct estimators like the sample mean have unacceptably large standard...

In this paper, we consider the problem of selecting the variables of the fixed effects in the linear mixed models where the random effects are present and the observation vectors have been obtained from many clusters. As the variable selection procedure, we here use the Akaike Information...

The Akaike Information Criterion (AIC) is developed for selecting the variables of a nested error regression model where an unobservable random effect is present. Using the idea of decomposing the marginal distribution into two parts of 'within' and 'between' analysis of variance, we derive the...

In the small area estimation, the empirical best linear unbiased predictor (EBLUP) in the linear mixed model is recognized useful because it gives a stable and reliable estimate for a mean of a small area. In practical situations where EBLUP is applied to real data, it is important to evaluate...

The Akaike information criterion, AIC, and Mallows' Cp statistic have been proposed for selecting a smaller number of regressor variables in the multivariate regression models with fully unknown covariance matrix. All these criteria are, however, based on the implicit assumption that the sample...

The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful for the small area estimation, because it can increase the estimation precision by using the information from the related areas. Two of the measures of...