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.
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Albers, W. A two-stage rank test using density estimation. Ann Inst Stat Math 47, 675–691 (1995). https://doi.org/10.1007/BF01856541
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DOI: https://doi.org/10.1007/BF01856541