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February 2000 Global power functions of goodness of fit tests
Arnold Janssen
Ann. Statist. 28(1): 239-253 (February 2000). DOI: 10.1214/aos/1016120371


It is shown that the global power function of any nonparametric test is flat on balls of alternatives except for alternatives coming from a finite dimensional subspace. The present benchmark is here the upper one-sided (or two-sided) envelope power function. Every choice of a test fixes a priori a finite dimensional region with high power. It turns out that also the level points are far away from the corresponding Neyman–Pearson test level points except for a finite number of orthogonal directions of alternatives. For certain submodels the result is independent of the underlying sample size. In the last section the statistical consequences and special goodness of fit tests are discussed.


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Arnold Janssen. "Global power functions of goodness of fit tests." Ann. Statist. 28 (1) 239 - 253, February 2000.


Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62329
MathSciNet: MR1762910
Digital Object Identifier: 10.1214/aos/1016120371

Primary: 62G10 , 62G20

Keywords: Bahadur efficiency , curvature of power functions , data driven Neyman’s smooth test, , envelope power function , goodness of fit test , intermediate efficiency. , Kolmogorov–Smirnov test , level points , Pitman efficiency , power function

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • February 2000
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