Optimal group sequential tests with groups of random size

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 form...

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Bibliographic Details
Published inSequential analysis Vol. 41; no. 2; pp. 220 - 240
Main Authors Novikov, A., Popoca-Jiménez, X. I.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.04.2022
Taylor & Francis Ltd
Subjects
Hypotheses
Hypothesis testing
optimal sequential tests
optimal stopping
sequential analysis
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ISSN0747-4946
1532-4176
DOI10.1080/07474946.2022.2070213

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Summary: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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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2022.2070213