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A TWO-STAGE RANK TEST USING DENSITY ESTIMATION

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WILLEM ALBERS

*Department of Applied Mathematics, University of Twente,*

P.O. Box 217, 7500 AE Enschede, The Netherlands
(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.

**Source**
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