Optimal Group-Sequential Tests with Groups of Random Size

TL;DR

This paper develops optimal sequential hypothesis tests for data received in randomly sized groups, minimizing observation costs while controlling error probabilities, under assumptions of independence and known group size distributions.

Contribution

It characterizes the structure of optimal tests for group-sequential hypothesis testing with random group sizes, balancing error control and observation costs.

Findings

Derived the structure of optimal tests under mild conditions.

Established methods to minimize average observation costs.

Provided theoretical guarantees for error probability constraints.

Abstract

We consider sequential hypothesis testing based on observations which 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 independently 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.