(Received February 28, 1994; revised March 31, 1995)
Abstract. For the one-sample problem, a two-stage rank test is derived which realizes a required power against a given local alternative, for all sufficiently smooth underlying distributions. This is achieved using asymptotic expansions resulting in a precision of order m-1, where m is the size of the first sample. The size of the second sample is derived through a number of estimators of e.g. integrated squared densities and density derivatives, all based on the first sample. The resulting procedure can be viewed as a nonparametric analogue of the classical Stein's two-stage procedure, which uses a t-test and assumes normality for the underlying distribution. The present approach also generalizes earlier work which extended the classical method to parametric families of distributions.
Key words and phrases: One-sample tests, local alternatives, Stein's two-stage procedure, Wilcoxon scores.