Asymptotically optimal multistage tests of simple hypotheses

TL;DR

This paper introduces a family of multistage testing procedures that optimize the trade-off between sampling costs and error probabilities, achieving near-optimal risk minimization as costs diminish, and outperforming traditional group sequential tests.

Contribution

It develops a new class of multistage tests based on efficient sampling procedures that minimize integrated risk to second order, improving upon existing methods.

Findings

Significant reduction in testing risk compared to group sequential tests

Optimality achieved as costs per stage and observation approach zero

Numerical results demonstrate practical improvements in binomial testing

Abstract

A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests are shown to minimize the integrated risk to second order as the costs per stage and per observation approach zero. A numerical study shows significant improvement over group sequential tests in a binomial testing problem.