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Hisayuki Tsukuma 《Statistical Papers》2012,53(4):915-934
The problem of simultaneously estimating location parameters is addressed, where the vector of location parameters belongs to a polyhedral cone including simple order, tree order and positive orthant restrictions and so forth. This paper proposes modified estimators based on orthogonal transformations such as sign-change and permutation and proves that, in a multivariate location family, the modified estimators are minimax under quadratic loss. Shrinkage minimax estimators improving on the modified estimators are obtained for a restricted mean vector of spherically symmetric distribution. An application of sign-change transformation is also given in estimation of a bounded normal mean. 相似文献
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This paper addresses the problem of estimating a matrix of the normal means, where the variances are unknown but common. The approach to this problem is provided by a hierarchical Bayes modeling for which the first stage prior for the means is matrix-variate normal distribution with mean zero matrix and a covariance structure and the second stage prior for the covariance is similar to Jeffreys’ rule. The resulting hierarchical Bayes estimators relative to the quadratic loss function belong to a class of matricial shrinkage estimators. Certain conditions are obtained for admissibility and minimaxity of the hierarchical Bayes estimators. 相似文献
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In this paper, the simultaneous estimation of the precision parameters of k normal distributions is considered under the squared loss function in a decision-theoretic framework. Several classes of minimax estimators are derived by using the chi-square identity, and the generalized Bayes minimax estimators are developed out of the classes. It is also shown that the improvement on the unbiased estimators is characterized by the superharmonic function. This corresponds to Stein's [1981. Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9, 1135–1151] result in simultaneous estimation of normal means. 相似文献
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We investigate the Bayes estimation of the means in Poisson decomposable graphical models. Some classes of Bayes estimators are provided which improve on the maximum likelihood estimator under the normalized squared error loss. Both proper and improper priors are included in the proposed classes of priors. Concerning the generalized Bayes estimators with respect to the improper priors, we address their admissibility. 相似文献
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This paper is concerned with the problem of constructing a good predictive distribution relative to the Kullback–Leibler information in a linear regression model. The problem is equivalent to the simultaneous estimation of regression coefficients and error variance in terms of a complicated risk, which yields a new challenging issue in a decision-theoretic framework. An estimator of the variance is incorporated here into a loss for estimating the regression coefficients. Several estimators of the variance and of the regression coefficients are proposed and shown to improve on usual benchmark estimators both analytically and numerically. Finally, the prediction problem of a distribution is noted to be related to an information criterion for model selection like the Akaike information criterion (AIC). Thus, several AIC variants are obtained based on proposed and improved estimators and are compared numerically with AIC as model selection procedures. 相似文献
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