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Inference for quantile measures of skewness

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  • Robert Staudte

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

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  • Robert Staudte, 2014. "Inference for quantile measures of skewness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 751-768, December.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:4:p:751-768
    DOI: 10.1007/s11749-014-0391-5
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    References listed on IDEAS

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    1. Frank Critchley & M. C. Jones, 2008. "Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 415-437, September.
    2. J. Rosco & M. Jones & Arthur Pewsey, 2011. "Skew t distributions via the sinh-arcsinh transformation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 630-652, November.
    3. Kulinskaya, Elena & Morgenthaler, Stephan & Staudte, Robert G., 2010. "Variance Stabilizing the Difference of Two Binomial Proportions," The American Statistician, American Statistical Association, vol. 64(4), pages 350-356.
    4. Stephan Morgenthaler & Robert G. Staudte, 2012. "Advantages of Variance Stabilization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 714-728, December.
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    Cited by:

    1. Miao, Xiaoyu & Wang, Qunwei & Dai, Xingyu, 2022. "Is oil-gas price decoupling happening in China? A multi-scale quantile-on-quantile approach," International Review of Economics & Finance, Elsevier, vol. 77(C), pages 450-470.
    2. Luke A. Prendergast & Robert G. Staudte, 2017. "When large n is not enough – Distribution-free interval estimators for ratios of quantiles," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(3), pages 277-293, September.
    3. Ahmed S & Sonia Pérez-F & Carlos Carleos A & Norberto C & Pablo Martínez C, 2018. "Inference in Stochastic Frontier Models Based on Asymmetry," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(4), pages 99-108, January.
    4. Luke A. Prendergast & Robert G. Staudte, 2017. "When large n is not enough – Distribution-free interval estimators for ratios of quantiles," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(3), pages 277-293, September.

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