The Annals of Statistics

Global power functions of goodness of fit tests

Arnold Janssen

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Abstract

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.

Article information

Source
Ann. Statist., Volume 28, Number 1 (2000), 239-253.

Dates
First available in Project Euclid: 14 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1016120371

Digital Object Identifier
doi:10.1214/aos/1016120371

Mathematical Reviews number (MathSciNet)
MR1762910

Zentralblatt MATH identifier
1106.62329

Subjects
Primary: 62G10: Hypothesis testing 62G20: Asymptotic properties

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

Citation

Janssen, Arnold. Global power functions of goodness of fit tests. Ann. Statist. 28 (2000), no. 1, 239--253. doi:10.1214/aos/1016120371. https://projecteuclid.org/euclid.aos/1016120371


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