## The Annals of Statistics

- Ann. Statist.
- Volume 19, Number 3 (1991), 1496-1511.

### Some Bootstrap Tests of Symmetry for Univariate Continuous Distributions

Miguel A. Arcones and Evarist Gine

#### Abstract

The Kolmogorov distance between the empirical $\operatorname{cdf} F_n$ and its symmetrization $sF_n$ with respect to an adequate estimator of the center of symmetry of $P$ is a natural statistic for testing symmetry. However, its limiting distribution depends on $P$. Using critical values from the symmetrically bootstrapped statistic (where the resampling is made from $sF_n$) produces tests that can be easily implemented and have asymptotically the correct levels as well as good consistency properties. This article deals with the asymptotic theory that justifies this procedure in particular for a test proposed by Schuster and Barker. Because of lack of smoothness (in some cases implying non-Gaussianness of the limiting processes), these tests do not seem to fall into existing general frameworks.

#### Article information

**Source**

Ann. Statist., Volume 19, Number 3 (1991), 1496-1511.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176348258

**Digital Object Identifier**

doi:10.1214/aos/1176348258

**Mathematical Reviews number (MathSciNet)**

MR1126334

**Zentralblatt MATH identifier**

0741.62042

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 62F10: Point estimation

**Keywords**

Tests of symmetry symmetric bootstrap bootstrap of location parameters

#### Citation

Arcones, Miguel A.; Gine, Evarist. Some Bootstrap Tests of Symmetry for Univariate Continuous Distributions. Ann. Statist. 19 (1991), no. 3, 1496--1511. doi:10.1214/aos/1176348258. https://projecteuclid.org/euclid.aos/1176348258