SOME BOOTSTRAP TESTS OF SYMMETRY FOR UNIVARIATE CONTINUOUS DISTRIBUTIONS

• 成果类型: Article
• 署名作者: ARCONES, MA; GINE, E
• 署名单位: City University of New York (CUNY) System; City University of New York (CUNY) System; College of Staten Island (CUNY)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348258
• 发表日期: 1991
• 页码: 1496-1511
• 关键词: STATISTICS; asymmetry; estimator

摘要

The Kolmogorov distance between the empirical 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.