A general measure of skewness

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• 作者：Magnus Ekströ ; m^a ; ^{Magnus.Ekstrom@slu.se} ; Sreenivasa Rao Jammalamadaka^b ; ^{rao@pstat.ucsb.edu}
• 关键词：Measure of skewness ; Bowley&rsquo ; s coefficient of skewness ; Test of symmetry ; Large sample theory ; Asymptotic relative efficiency
• 刊名：Statistics and Probability Letters
• 出版年：2012
• 期刊代码：56_01677152
• 类别：mt
• 出版时间：August, 2012
• 卷：82
• 期：8
• 页码：1559-1568
• 文件大小：278 K

摘要

A very general measure of skewness based on the quantiles is introduced, which includes several well-known measures as special cases. Sample versions of our measure may be used as test statistics for testing the hypothesis of symmetry about an unknown value. We provide large sample theory for such a statistic and discuss the asymptotic relative efficiencies of this against some competing test statistics for symmetry.