The Annals of Statistics

Bootstrap and Randomization Tests of some Nonparametric Hypotheses

Joseph P. Romano

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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.

Article information

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

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347007

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176347007

Mathematical Reviews number (MathSciNet)
MR981441

Zentralblatt MATH identifier
0688.62031

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

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

Citation

Romano, Joseph P. Bootstrap and Randomization Tests of some Nonparametric Hypotheses. The Annals of Statistics 17 (1989), no. 1, 141--159. doi:10.1214/aos/1176347007. http://projecteuclid.org/euclid.aos/1176347007.


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