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131.
Dipak K. Dey 《统计学通讯:理论与方法》2013,42(6):661-673
The problem of choice of coordinates in Stein-type estimators,when simultaneously estimating normal means, is considered. The question of deciding whether to use all coordinates in one combined shrinkage estimators or to separate into groups and use separate shrinkage estimators on each group is considered in the situation in which part of the prior information may be " misspecified". It is observed that the amount of misspecification determines whether to use the combined shrinkage estimator the separate shrinkage estimator. 相似文献
132.
Robert L. Obenchain 《统计学通讯:理论与方法》2013,42(2):227-240
I illustrate likelihood methods for estimating the consequences of shrinkage along any ridge path as well as methods for picking a two-hyperparameter path of optimal curvature and the optimal point on that path. In addition to my published "classical" methods, I also illustrate both the empirical Bayes and the random coefficient maximum likelihood approaches. Traces of risks for known parameters and losses for simulated responses are followed by traces of estimates that can reveal the same general information. 相似文献
133.
T.W.F. Stroud 《统计学通讯:理论与方法》2013,42(17):2085-2109
For a linear regression model over m populations with separate regression coefficients but a common error variance, a Bayesian model is employed to obtain regression coefficient estimates which are shrunk toward an overall value. The formulation uses Normal priors on the coefficients and diffuse priors on the grand mean vectors, the error variance, and the between-to-error variance ratios. The posterior density of the parameters which were given diffuse priors is obtained. From this the posterior means and variances of regression coefficients and the predictive mean and variance of a future observation are obtained directly by numerical integration in the balanced case, and with the aid of series expansions in the approximately balanced case. An example is presented and worked out for the case of one predictor variable. The method is an extension of Box & Tiao's Bayesian estimation of means in the balanced one-way random effects model. 相似文献
134.
Peter J. Kempthorne 《统计学通讯:理论与方法》2013,42(7):2145-2157
Minimax squared error risk estimators of the mean of a multivariate normal distribution are characterized which have smallest Bayes risk with respect to a spherically symmetric prior distribution for (i) squared error loss, and (ii) zero-one loss depending on whether or not estimates are consistent with the hypothesis that the mean is null. In (i), the optimal estimators are the usual Bayes estimators for prior distributions with special structure. In (ii), preliminary test estimators are optimal. The results are obtained by applying the theory of minimax-Bayes-compromise decision problems. 相似文献
135.
Let πi(i=1,2,…K) be independent U(0,?i) populations. Let Yi denote the largest observation based on a random sample of size n from the i-th population. for selecting the best populaton, that is the one associated with the largest ?i, we consider the natural selection rule, according to which the population corresponding to the largest Yi is selected. In this paper, the estimation of M. the mean of the selected population is considered. The natural estimator is positively biased. The UMVUE (uniformly minimum variance unbiased estimator) of M is derived using the (U,V)-method of Robbins (1987) and its asymptotic distribution is found. We obtain a minimax estimator of M for K≤4 and a class of admissible estimators among those of the form cYmax. For the case K = 2, the UMVUE is improved using the Brewster-Zidek (1974) Technique with respect to the squared error loss function L1 and the scale-invariant loss function L2. For the case K = 2, the MSE'S of all the estimators are compared for selected values of n and ρ=?1/(?1+?2). 相似文献
136.
The relative 'performances of improved ridge estimators and an empirical Bayes estimator are studied by means of Monte Carlo simulations. The empirical Bayes method is seen to perform consistently better in terms of smaller MSE and more accurate empirical coverage than any of the estimators considered here. A bootstrap method is proposed to obtain more reliable estimates of the MSE of ridge esimators. Some theorems on the bootstrap for the ridge estimators are also given and they are used to provide an analytical understanding of the proposed bootstrap procedure. Empirical coverages of the ridge estimators based on the proposed procedure are generally closer to the nominal coverage when compared to their earlier counterparts. In general, except for a few cases, these coverages are still less accurate than the empirical coverages of the empirical Bayes estimator. 相似文献
137.
In the present paper we have proposed a Bayesian approach for making inferences from accelerated life tests which do not require distributional assumptions 相似文献
138.
139.
Paul Chiou 《统计学通讯:理论与方法》2013,42(5):1483-1494
In this paper we propose two empirical Bayes shrinkage estimators for the reliability of the exponential distribution and study their properties. Under the uniform prior distribution and the inverted gamma prior distribution these estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. The proposed empirical Bayes shrinkage estimator under the inverted gamma prior distribution is shown to be preferable to the preliminary test estimator and the shrinkage testimator when the prior value of mean life is clsoe to the true mean life. 相似文献
140.
A modified double stage shrinkage estimator has been proposed for the single parameter θ of a distribution function Fθ. It is shown to be locally better in comparison to the usual double stage shrinkage estimator in the sense of smaller mean squared error in a certain neighbourhood of prior estimate θo of θ. 相似文献