Asymptotic optimality of a robust two-stage procedure in multivariate Bayes sequential estimation

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2023-01-02 DOI:10.1080/07474946.2022.2154364

Leng-Cheng Hwang

引用次数: 0

Abstract

Abstract Within the Bayesian framework, a robust two-stage procedure is proposed to deal with the problem of multivariate sequential estimation of the unknown mean vector with weighted squared error loss and fixed cost per observation. The proposed procedure depends on the present data but not on the distributions of outcome variables or the prior. It is shown that the proposed procedure shares the asymptotic properties with the optimal fixed-sample-size procedures for the arbitrary distributions and the asymptotically pointwise optimal procedures for the distributions of a multivariate exponential family with a large class of prior distributions. Simulation results indicate that the proposed two-stage procedure is robust to misspecification of the true parameters of the prior distribution and outperforms the purely sequential procedure and the asymptotically pointwise optimal procedure in terms of robustness.

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多元贝叶斯序列估计中稳健两阶段过程的渐近最优性

摘要在贝叶斯框架下，提出了一种鲁棒的两阶段方法来处理具有加权平方误差损失和固定每次观测代价的未知均值向量的多变量序列估计问题。所建议的程序取决于当前的数据，而不取决于结果变量的分布或先验。结果表明，该过程与任意分布的最优固定样本大小过程和具有大量先验分布的多元指数族分布的渐近点向最优过程具有相同的渐近性质。仿真结果表明，所提出的两阶段方法对先验分布真实参数的错误规范具有较强的鲁棒性，鲁棒性优于纯序列方法和渐近点优化方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.