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An Asymptotic Second-Order Lower Bound for the Bayes Risk of a Sequential Procedure

机译：顺序程序的贝叶斯风险的渐近二阶下界

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摘要

Consider the problem of estimating the difference of the means of two populations, where each population distribution is a member of the one-parameter exponential family of probability distributions. A Bayesian approach is adopted in which the mean difference is estimated under the squared error loss and the prior distributions are of the form proposed by Diaconis and Ylivisaker [Diaconis, P.; Ylivisaker, D. Conjugate priors for exponential families. Ann. of Statist. 1979, 6, 269-281]. The main result determines an asymptotic second-order lower bound for the Bayes risk of a sequential procedure that takes N observations from one population and t — N from the other population, and estimates the mean difference by the Bayes estimator, where N is determined according to a sequential design and t denotes the total number of observations sampled from both populations.
机译：考虑估计两个总体的均值差的问题，其中每个总体分布都是概率分布的一参数指数族的成员。采用贝叶斯方法，其中在均方差损失下估计均值差，并且先验分布具有Diaconis和Ylivisaker提出的形式[Diaconis，P; Ylivisaker，D.为指数族共轭先验。安统计员。 1979，6，269-281]。主要结果确定了顺序过程的Bayes风险的渐近二阶下界，该过程取自一个种群的N个观测值和来自另一种群的t_N个观测值，并由Bayes估计量估计均值差，其中N是根据表示顺序设计，t表示从两个总体中抽样的观察总数。

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