Inference for quantile measures of skewness

Robert Staudte ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2014, vol. 23, issue 4, 768 pages

Abstract: Given a location-scale family generated by a distribution with smooth positive density, the aim is to provide distribution-free tests and confidence intervals for a skewness coefficient determined by three quantiles. It is the Bowley–Hinkley ratio $$S_r/R_r$$ S r / R r , where $$S_r=x_r+x_{1-r}-2x_{0.5}$$ S r = x r + x 1 - r - 2 x 0.5 is the sum of two symmetric quantiles minus twice the median, and $$R_r=x_{1-r}-x_r$$ R r = x 1 - r - x r is the $$r$$ r th interquantile range. Here, $$0>r> 0.5$$ 0 > r > 0.5 is to be chosen and fixed. The sample version of this ratio depends only on three order statistics and is the basis for tests and confidence intervals. It is shown that the variance stabilized version of this statistic leads to more powerful tests than the Studentized version of the sample version of $$S_r$$ S r . Sample sizes required to obtain accurate coverage of confidence intervals with a prespecified width are provided. Copyright Sociedad de Estadística e Investigación Operativa 2014

Keywords: Bowley’s coefficient of skewness; Distribution-free confidence intervals; Power functions; Tests for symmetry; Tukey’s sparsity index; 62G99 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11749-014-0391-5

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