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A two-stage rank test using density estimation
Authors:Willem Albers
Institution:(1) Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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 orderm –1, wherem 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 at-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.
Keywords:One-sample tests  local alternatives  Stein's two-stage procedure  Wilcoxon scores
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