A new asymptotic distribution for Hollander's bivariate symmetry statistic.
type: Item
instance of: scholarly article
title: A new asymptotic distribution for Hollander's bivariate symmetry statistic.
zbMATH Open document ID: 1061.62515
DOI: 10.1016/S0167-9473(99)00093-6
published in: Computational Statistics and Data Analysis
publication date: 2000-06-04T00:00:00Z
review text: We show that the asymptotic distribution [\textit{J. A. Koziol}, Commun. Stat., Theory Methods A8, 207--221 (1979; Zbl 0445.62063)] of the bivariate symmetry statistic standardized by \(1/n^{3}\), where \(n\) is the number of iid paired observations from bivariate distribution F, fails to account for the conditional nature of the statistic and is very conservative for all n. We describe the dependence of the true critical values of the test on the covariance of the paired samples, \(\sigma_{xy}\), which is a nuisance parameter in this problem. We propose an alternative standardization of the bivariate symmetry statistic that adjusts it for \(\sigma_{xy}\) as well as n. We show via a simulation study that the size of the proposed asymptotic test is close to the nominal level, even for small n.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 1454528
zbMATH Keywords: Paired data
zbMATH Keywords: Bivariate exchangeability hypothesis
zbMATH Keywords: Validity
author: Joan F. Hilton
MaRDI profile type: Publication
cites work: An Exact Hollander Bivariate Symmetry Test
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cites work: Q4704222
cites work: Comparison of tests for bivariate symmetry versus location and/or scale alternatives
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description: scientific article; zbMATH DE number 1454528