## The Annals of Statistics

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

### Bootstrap and Randomization Tests of some Nonparametric Hypotheses

#### 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 in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176347007

**Digital Object Identifier**

doi:10.1214/aos/1176347007

**Mathematical Reviews number (MathSciNet)**

MR981441

**Zentralblatt MATH identifier**

0688.62031

**JSTOR**

links.jstor.org

**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. Ann. Statist. 17 (1989), no. 1, 141--159. doi:10.1214/aos/1176347007. http://projecteuclid.org/euclid.aos/1176347007.