共查询到20条相似文献,搜索用时 31 毫秒
1.
Rohana J. Karunamuni 《Annals of the Institute of Statistical Mathematics》1996,48(4):711-730
We consider the empirical Bayes decision problem where the component problem is the sequential estimation of the mean of one-parameter exponential family of distributions with squared error loss for the estimation error and a cost c>0 for each observation. The present paper studies the untruncated sequential component case. In particular, an untruncated asymptotically pointwise optimal sequential procedure is employed as the component. With sequential components, an empirical Bayes decision procedure selects both a stopping time and a terminal decision rule for use in the component with parameter . The goodness of the empirical Bayes sequential procedure is measured by comparing the asymptotic behavior of its Bayes risk with that of the component procedure as the number of past data increases to infinity. Asymptotic risk equivalence of the proposed empirical Bayes sequential procedure to the component procedure is demonstrated.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant GP7987. 相似文献
2.
Dennis C. Gilliland Rohana Karunamuni 《Annals of the Institute of Statistical Mathematics》1988,40(1):187-193
Laippala (1979, Scand. J. Statist., 6, 113–118, correction note, 7, 105; 1985, Ann. Inst. Statist. Math., 37, 315–327) has defined a concept within the empirical Bayes framework that he calls floating optimal sample size. We examine this concept and show that it is one of many possibilities resulting from restricting the class of component sampling procedures in the empirical Bayes decision problem with a sequential component. All ideas are illustrated with the finite state component. 相似文献
3.
In this paper, the empirical Bayes (EB) two-sided test for parameter of Cox models is investigated under square loss functions. At first by using recursive kernel estimation of probability function the empirical Bayes two-sided test rule is constructed. It proves that the proposed empirical Bayes test rule is asymptotic optimal and convergence rates are obtained under suitable conditions. Finally an example of satisfying theorem conditions is given. 相似文献
4.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-4):285-293
The concept of statistical decision theory concerning sequential observations is generalized to decision problems, which are based upon a continuous stochastic process. In this model decision functions are introduced, consisting of a stopping time and a terminal decision rule. A method of discretization shows the connections between the discrete sequential and the continuous model. Concerning Bayes problems we find, that under certain assumptions the decision problem can be viewed as an optimal stopping problem with continuous time parameter. 相似文献
5.
Pekka Laippala 《Annals of the Institute of Statistical Mathematics》1985,37(1):315-327
Summary We consider the empirical Bayes solution in such a situation where the sample size is successively determined by a rule which
includes the Bayes risks and the observation costs. The empirical Bayes floating optimal sample size depends on current as
well as on previous information assumed to be collected from earlier performances of similar decisions. The sampling is done
from an exponential conditional distribution, with a single parameter. The proofs, which show the asymptotic optimality of
the empirical Bayes solution, are presented for a hypotheses-testing problem. A straight generalization to a multiple decision
problem is also given. 相似文献
6.
7.
本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性. 相似文献
8.
Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n^-1/2). Finally, an example concerning the main result is given. 相似文献
9.
《Statistics & probability letters》1985,3(6):309-313
In the empirical Bayes (EB) decision problem consisting of squared error estimation of a Poisson mean, a prior distribution λ is placed on the gamma family of prior distributions to produce Bayes EB estimators which are admissible. A subclass of such estimators is shown to be asymptotically optimal (a.o.). The results of a Monte Carlo study are presented to demonstrate the favorable a.o. property of the Bayes EB estimators in comparison with other competitors. 相似文献
10.
随机效应模型中方差分量的经验Bayes检验问题 总被引:4,自引:0,他引:4
给出了双向分类随机效应模型中方差分量的Bayes检验的判决函数,利用核估计的方法,构造了相应的经验Bayes(EB)检验的判决函数.在适当的条件下证明了EB判决函数是渐近最优的且有收敛速度.给出了模型的特例和推广.最后,举出一个满足定理条件的例子. 相似文献
11.
本文讨论了在纵向数据下,运用非参数估计方法构造了连续型单参数指数族参数的经验贝叶斯检验函数,证明了所提出的经验贝叶斯检验函数的渐近最优性,并获得了它的收敛速度. 相似文献
12.
Christophe Abraham 《Journal of multivariate analysis》2001,79(2):251
Similarly to the determination of a prior in Bayesian Decision theory, an arbitrarily precise determination of the loss function is unrealistic. Thus, analogously to global robustness with respect to the prior, one can consider a set of loss functions to describe the imprecise preferences of the decision maker. In this paper, we investigate the asymptotic behavior of the Bayes actions set derived from a class of loss functions. When the collection of additional observations induces a decrease in the range of the Bayes actions, robustness is improved. We give sufficient conditions for the convergence of the Bayes actions set with respect to the Hausdorff metric and we also give the limit set. Finally, we show that these conditions are satisfied when the set of decisions and the set of states of nature are subsets of
p. 相似文献
13.
Huang Juan 《东北数学》2011,27(1):17-23
For the data with error of measurement in historical samples, the empirical Bayes test rule for the parameter of Rayleigh distribution is constructed, and the asymptotically optimal property is obtained. It is shown that the convergence rate of the proposed EB test rule can be arbitrarily close to O(n-1/2) under suitable conditions. 相似文献
14.
《Journal of computational and graphical statistics》2013,22(4):772-785
We observe n events occurring in (0, T] taken from a Poisson process. The intensity function of the process is assumed to be a step function with multiple changepoints. This article proposes a Bayesian binary segmentation procedure for locating the changepoints and the associated heights of the intensity function. We conduct a sequence of nested hypothesis tests using the Bayes factor or the BIC approximation to the Bayes factor. At each comparison in the binary segmentation steps, we need only to compare a singlechangepoint model to a no-changepoint model. Therefore, this method circumvents the computational complexity we would normally face in problems with an unknown (large) number of dimensions. A simulation study and an analysis on a real dataset are given to illustrate our methods. 相似文献
15.
利用经验Bayes方法,我们提出了一套选择带控制的最优Logistic总体的方案,并给出了择优统计量的收敛速度. 相似文献
16.
Khursheed Alam James R. Thompson 《Annals of the Institute of Statistical Mathematics》1969,21(1):457-469
Summary A heuristic method of reducing a class of admissible or Bayes decision rules is given. A new risk function is defined which
is called the locally averaged risk. Bayes and admissible rules with respect to the new risk function are calledG-Bayes andG-admissible, respectively. It is shown under general assumptions that the class ofG-Bayes decision rules is a subset of the class of Bayes decision rules and the class ofG-admissible decision rules is a subset of the class of admissible decision rules.
Some examples are considered, showing that the usual estimates of the parameter of a distribution with squared error as loss
function, which are known to be admissible, are alsoG-admissible.
This work was supported in part by NASA Grant-NGR 15-003-064 and NSF Grant-GP 7496 at Indiana University. 相似文献
17.
Ester Samuel 《Israel Journal of Mathematics》1965,3(3):117-126
The compound decision problem is considered under the assumption that Nature plays the role of an opponent. The empirical
Bayes approach is a particular case of this approach. It is shown that in many instances sequential compound rules with good
asymptotic properties for the fixed case have similar good properties in the opponent case. 相似文献
18.
几何分布时间序贯检验的贝叶斯推断 总被引:13,自引:1,他引:12
设有统计模型{x,Bx,Pθ},θ∈(0,1),其中Pθ为几何分布:Pθ(X=k)=(1-θ)θ^k-1k=1,2,…。考虑检验问题:θ=θo vs. θ=θ1(0〈θ0〈θ1〈1)本文对一种依次试验的时间序贯样本,给出了上述检验问题的贝叶斯停止判决法则,其中损失函数为试验费用和误判损失之和,贝叶斯停止判决法则由后验概率的两组界(上界和下界)所给出。 相似文献
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20.
Arthur Cohen 《Journal of multivariate analysis》2007,98(3):481-492
Cohen and Sackrowitz [Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure, Ann. Statist. 33 (2005) 145-158] proved that the step-up multiple testing procedure is inadmissible for a multivariate normal model with unknown mean vector and known intraclass covariance matrix. The hypotheses tested are each mean is zero vs. each mean is positive. The risk function is a 2×1 vector where one component is average size and the other component is one minus average power. In this paper, we extend the inadmissibility result to several different models, to two-sided alternatives, and to other risk functions. The models include one-parameter exponential families, independent t-variables, independent χ2-variables, t-tests arising from the analysis of variance, and t-tests arising from testing treatments against a control. The additional risk functions are linear combinations where one component is the false discovery rate (FDR). 相似文献