Asymptotic Optimality in Sequential interval Estimation

Beginning with Stein’s [9] two stage procedure, there has been substantial interest in the use of sequential methods to set a fixed width confidence interval for the mean of a distribution with unknown variance. This interest was stimulated by the fully sequential procedures of Anscombe [l] and Chow and Robbins [2] for the normal and non-parametric cases, and continues today. The recent work of Hall [5] and Finster [4] is especially noteworthy and may be consulted for further references. The emphasis of much of this work has been the construction of sequential sampling plans for which the probability that the sample and population means differ by less than a prescribed h > 0 is large, at least of prescribed y, and the comparison of the expected sample sizes of such plans with the hypothetical fixed sample size which would be required if the variance were known. The plans effectively estimate the hypothetical fixed sample size as data accumulate and stop when the sample size exceeds the