Open Access
March, 1989 Bootstrap and Randomization Tests of some Nonparametric Hypotheses
Joseph P. Romano
Ann. Statist. 17(1): 141-159 (March, 1989). DOI: 10.1214/aos/1176347007

Abstract

In this paper, the asymptotic behavior of some nonparametric tests is studied in situations where both bootstrap tests and randomization tests are applicable. Under fairly general conditions, the tests are asymptotically equivalent in the sense that the resulting critical values and power functions are appropriately close. This implies, among other things, that the difference in the critical functions of the tests, evaluated at the observed data, tends to 0 in probability. Randomization tests may be preferable since an exact desired level of the test may be obtained for finite samples. Examples considered are: testing independence, testing for spherical symmetry, testing for exchangeability, testing for homogeneity, and testing for a change point.

Citation

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Joseph P. Romano. "Bootstrap and Randomization Tests of some Nonparametric Hypotheses." Ann. Statist. 17 (1) 141 - 159, March, 1989. https://doi.org/10.1214/aos/1176347007

Information

Published: March, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0688.62031
MathSciNet: MR981441
Digital Object Identifier: 10.1214/aos/1176347007

Subjects:
Primary: 62G10
Secondary: 62E20 , 62G30

Keywords: bootstrap , nonparametric tests , randomization tests , testing equality of distributions , testing for rotational invariance , testing independence , Vapnik-Cervonenkis classes

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • March, 1989
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