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, here we use the Akaike Information...

In the problem of selecting the explanatory variables in the linear mixed model, we address the derivation of the (unconditional or marginal) Akaike information criterion (AIC) and the conditional AIC (cAIC). The covariance matrices of the random effects and the error terms include unknown...

The empirical Bayes (EB) estimator or empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation in the sense of increasing the precision of estimation of small area means. However, one potential difficulty of EB is that when...

Consider the problem of testing a linear hypothesis of regression coefficients in a general linear regression model with a covariance matrix involving several nuisance parameters. Then, the Bartlett-type adjustments of the Wald, Score, and modified Likelihood Ratio tests are derived for general...

In this paper, we suggest the new variable selection procedure, called MEC, for linear discriminant rule in the high dimensional and large sample setup. MEC is derived as a second-order unbiased estimator of the misclassification error probability of the linear discriminant rule (LDR). It is...

The problem of classifying a new observation vector into one of the two known groups distributed as multivariate normal with common covariance matrix is considered. In this paper, we handle the situation that the dimension, p, of the observation vectors is less than the total number, N, of...

For the quadratic loss function, it is shown that the best affine equivariant estimator of the normal covariance matrix is improved on by Stein-type estimators.

Banks are recognized as playing an important role of monitoring borrowers, thereby reducing the agency costs associated with informational asymmetry. However, there remains an issue "who could monitor the banks", because it is difficult for outsiders to monitor banks' management. In particular,...

This paper discusses a novel estimation method for the residential gas demand function in Japan where the price per unit decreases as the demand exceeds certain thresholds. Such a price system is known as decreasing block rate pricing. The demand function under decreasing block rate pricing is...