SAMPLE-SIZE-OPTIMAL SEQUENTIAL TESTING

Sequential sampling schemes have traditionally used ad hoc rules for sample size. The variable-sample-size sequential probability ratio test (VPRT), developed by Cressie and Morgan (Proc. 4th Purdue Symp. on Decision Theory and Related Topics, IV Vol. 2, Springer, New York (1988), 107-118), generalizes the classical one-at-a-time and group-sequential procedures to an optimal procedure that maximizes the expected net gain of sampling, conditional on the accumulated observations on the stochastic process. In this paper, we apply the VPRT to the problem of sequential testing of a Gaussian mean.