Optimal group sequential tests with groups of random size

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.

Keywords:

• Hypothesis testing
• optimal sequential tests
• optimal stopping
• sequential analysis

SUBJECT CLASSIFICATIONS:

• 62L10
• 62L15
• 62F03
• 60G40

ACKNOWLEDGMENTS

The authors are grateful to the anonymous reviewers and editors for their valuable comments that contributed to the improvement of this work.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

A. Novikov thanks SNI by CONACyT, Mexico, for partial support for this work. X. I. Popoca-Jiménez thanks CONACyT, Mexico, for scholarships for her studies.