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September, 1991 Some Bootstrap Tests of Symmetry for Univariate Continuous Distributions
Miguel A. Arcones, Evarist Gine
Ann. Statist. 19(3): 1496-1511 (September, 1991). DOI: 10.1214/aos/1176348258


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.


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Miguel A. Arcones. Evarist Gine. "Some Bootstrap Tests of Symmetry for Univariate Continuous Distributions." Ann. Statist. 19 (3) 1496 - 1511, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62042
MathSciNet: MR1126334
Digital Object Identifier: 10.1214/aos/1176348258

Primary: 62G10
Secondary: 62F10

Keywords: bootstrap of location parameters , symmetric bootstrap , Tests of symmetry

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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