## The Annals of Statistics

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

#### 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

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