Sequential Tests of Statistical Hypotheses with Confidence Limits

摘要

In this paper, we propose a general method for testing composite hypotheses.Our idea is to use confidence limits to define stopping and decision rules. Therequirements of operating characteristic function can be satisfied by adjustingthe coefficients of the confidence limits. For common distributions, suchadjustment can be done via efficient computation by making use of themonotonicity of the associated operating characteristic function. We show thatthe problem of testing multiple hypotheses can be cast into the generalframework of constructing sequential random intervals with prescribed coverageprobabilities. We propose an inclusion principle for constructing multistagetesting plans. It is demonstrated that our proposed testing plans can besubstantially more efficient than the sequential probability ratio test and itsvariations. We apply our general methodology to develop an exact approach fortesting hypotheses regarding the difference of two binomial proportions.