Consecutive Sequential Probability Ratio Tests of Multiple Statistical Hypotheses

TL;DR

This paper introduces a straightforward method for sequentially testing multiple hypotheses using probability ratios, providing explicit bounds on error probabilities and generalizing Wald's SPRT for two hypotheses.

Contribution

It develops a simple, unified approach for multiple hypothesis testing with tight error bounds, extending classical SPRT to multiple hypotheses.

Findings

Derived explicit bounds for decision error probabilities.

Unified framework generalizing Wald's SPRT to multiple hypotheses.

Applicable to sequential testing scenarios with controlled error rates.

Abstract

In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds for the probability of making wrong decisions are obtained for choosing appropriate parameters for the proposed tests. In the special case of testing two hypotheses, our tests reduce to Wald's sequential probability ratio tests.