Estimation after sequential testing: A simple approach for a truncated sequential probability ratio test

Abstract

SUMMARY An approximate pivot is constructed for the problem of estimating a normal mean θ following a truncated sequential probability ratio test and shown to provide a useful method for constructing confidence bounds and intervals. Letting t denote the sample size and S 1 the sum of observations, the approximate pivot is constructed by standardizing S * t =t−½(S t −tθ) the mean and variance of which are no longer 0 and 1, due to the optional stopping. The truncation of the sequential probability ratio test is done in a nonstandard way in order to smooth the boundary.