The Annals of Statistics

Bootstrap and Randomization Tests of some Nonparametric Hypotheses

Joseph P. Romano

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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.

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Ann. Statist., Volume 17, Number 1 (1989), 141-159.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62G10: Hypothesis testing
Secondary: 62E20: Asymptotic distribution theory 62G30: Order statistics; empirical distribution functions

Bootstrap nonparametric tests randomization tests testing independence testing equality of distributions testing for rotational invariance Vapnik-Cervonenkis classes


Romano, Joseph P. Bootstrap and Randomization Tests of some Nonparametric Hypotheses. Ann. Statist. 17 (1989), no. 1, 141--159. doi:10.1214/aos/1176347007.

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