Optimal group sequential tests with groups of random size

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2021-10-08 DOI:10.1080/07474946.2022.2070213

A. Novikov, X. I. Popoca-Jiménez

引用次数: 3

Abstract

Abstract We consider sequential hypothesis testing based on observations that are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent and their distributions are known and that the groups are formed independent of the observations. We are concerned with a problem of testing a simple hypothesis against a simple alternative. For any (group) sequential test, we take into account the following three characteristics: its type I and type II error probabilities and the average cost of observations. Under mild conditions, we characterize the structure of sequential tests minimizing the average cost of observations among all sequential tests whose type I and type II error probabilities do not exceed some prescribed levels.

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随机分组的最优分组序列检验

摘要我们考虑基于以随机大小的组接收的观察结果的顺序假设检验。假设观察结果在小组内部和小组之间是独立的。我们假设群的大小是独立的，它们的分布是已知的，并且群的形成与观测无关。我们关注的是一个简单假设与简单替代方案的检验问题。对于任何（组）序列检验，我们考虑以下三个特征：其I型和II型错误概率以及观察的平均成本。在温和的条件下，我们描述了序列测试的结构，在所有I型和II型错误概率不超过某些规定水平的序列测试中，使观测的平均成本最小化。

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.