Stopping Times of Two Rank Order Sequential Probability Ratio Tests for Symmetry Based on Lehmann Alternatives

摘要

Two, modified, one-sample, rank order SPRT's for symmetry based on Lehmann alternatives are given. The first model (Model I) is discussed by Weed and Bradley (1969) and Weed (1968); the second model (Model II) was proposed by Govindarajulu (1968) and is developed here. The two models depend on two different choices of Lehmann alternatives. The results of this paper were developed independently but, as proofs are essentially the same, the authors have combined their work. It is shown, under very general conditions, that the two procedures terminate with probability one and the moments of stopping times are finite for all alternatives within the classes of alternatives defined by Models I and II. Further, procedures based on approximate probability ratios are also studied when the distribution function at zero under the alternative hypothesis is unknown but estimated from the sample observations. (Author)