Confidence intervals following sequential tests

Abstract

This thesis is concerned with obtaining confidence intervals following onesided sequential tests. The method involves defining an order relation among points on the stopping boundary and computing the probability of a deviation more extreme in this order relation than the observed ones. In the sequential tests, we have to find the probabilities that the tests terminate within a specified number of stages to compute the confidence intervals following the tests. There are some special cases, such as uniform distribution, where these probabilities can be determined exactly. In those cases, we can compute confidence intervals without approximations. In general, however, very little is known about these probabilities, and approximate expressions for the first four moments of the decisive sample number are used to evaluate these probabilities approximately. We also give numerical examples for normal, exponential, and Poisson distributions and compute the related confidence intervals.