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指数分布族参数的渐近最优与可容许的经验Bayes估计 总被引:2,自引:1,他引:2
在平方损失下 ,构造了指数族 { f(x|λ) =λe-λx,λ >0 ,x >0 }的参数λ的渐近最优与可容许的经验Bayes估计 ,即δn=(n +u + 1n1φ(n) + 1) β1+ βX,其中X1,X2 ,…Xn(历史样本 )和X(当前样本 )独立同分布于 f(x) ,Sn= ni=11n(1+ βXi) ,φ(n) =1n(Sn+ 1n(1+ βX) +v- 1) ,u >0 ,v >0 ,β >0 (已知 )为任意的实数 ,并证明了该估计的收敛速度为O(n- 1)。 相似文献
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Khursheed Alam 《Annals of the Institute of Statistical Mathematics》1984,36(1):51-58
Summary The Bayes method is seldom applied to nonparametric statistical problems, for the reason that it is hard to find mathematically
tractable prior distributions on a set of probability measures. However, it is found that the Dirichlet process generates
randomly a family of probability distributions which can be taken as a family of prior distributions for an application of
the Bayes method to such problems. This paper presents a Bayesian analysis of a nonparametric problem of selecting a distribution
with the largestpth quantile value, fromk≧2 given distributions. It is assumed a priori that the given distributions have been generated from a Dirichlet process.
This work was supported by the U.S. Office of Naval Research under Contract No. 00014-75-C-0451. 相似文献
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本文讨论了连续型单参数指数族的经验Bayes检验问题 .利用核估计方法构造了EB检验函数并获得了它的收敛速度 . 相似文献
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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