ESTIMATION AFTER SEQUENTIAL TESTING - A SIMPLE APPROACH FOR A TRUNCATED SEQUENTIAL PROBABILITY RATIO TEST

An approximate pivot is constructed for the problem of estimating a normal mean-theta 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, the sum of observations, the approximate pivot is constructed by standardizing S(t)* = t-1/2(S(t) - t-theta) 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.