Multistage Hypothesis Tests for the Mean of a Normal Distribution

TL;DR

This paper introduces new multistage hypothesis tests for the mean of a normal distribution that are more efficient and have bounded maximum sample sizes, using geometric bounds and adaptive algorithms.

Contribution

It presents novel multistage tests with guaranteed power, bounded maximum samples, and efficient computation methods based on geometric and adaptive techniques.

Findings

Tests are more efficient than previous methods.

Maximum sampling numbers are absolutely bounded.

Adaptive algorithms reduce computational complexity.

Abstract

In this paper, we have developed new multistage tests which guarantee prescribed level of power and are more efficient than previous tests in terms of average sampling number and the number of sampling operations. Without truncation, the maximum sampling numbers of our testing plans are absolutely bounded. Based on geometrical arguments, we have derived extremely tight bounds for the operating characteristic function. To reduce the computational complexity for the relevant integrals, we propose adaptive scanning algorithms which are not only useful for present hypothesis testing problem but also for other problem areas.