IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v23y2014i4p751-768.html
   My bibliography  Save this article

Inference for quantile measures of skewness

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11749-014-0391-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11749-014-0391-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    4. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    5. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    6. Rubio, Francisco Javier & Steel, Mark F. J., 2014. "Bayesian modelling of skewness and kurtosis with two-piece scale and shape transformations," MPRA Paper 57102, University Library of Munich, Germany.
    7. 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.
    8. David R. Bickel, 2021. "The sufficiency of the evidence, the relevancy of the evidence, and quantifying both with a single number," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1157-1174, October.
    9. Rui Li & Saralees Nadarajah, 2020. "A review of Student’s t distribution and its generalizations," Empirical Economics, Springer, vol. 58(3), pages 1461-1490, March.
    10. A. Arriaza & A. Crescenzo & M. A. Sordo & A. Suárez-Llorens, 2019. "Shape measures based on the convex transform order," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 99-124, January.
    11. Giri Parameswaran & Hunter Rendleman, 2022. "Redistribution under general decision rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(1), pages 159-196, February.
    12. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    13. Andreas Eberl & Bernhard Klar, 2022. "Expectile‐based measures of skewness," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 373-399, March.
    14. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    15. Jones, M.C., 2012. "Relationships between distributions with certain symmetries," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1737-1744.
    16. Andreas Eberl & Bernhard Klar, 2021. "A note on a measure of asymmetry," Statistical Papers, Springer, vol. 62(3), pages 1483-1497, June.
    17. P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
    18. Irène Gijbels & Rezaul Karim & Anneleen Verhasselt, 2020. "Response to the Letter to the Editor on ‘On Quantile‐based Asymmetric Family of Distributions: Properties and Inference’," International Statistical Review, International Statistical Institute, vol. 88(3), pages 797-801, December.
    19. Xu, Zhongxiang & Chevapatrakul, Thanaset & Li, Xiafei, 2019. "Return asymmetry and the cross section of stock returns," Journal of International Money and Finance, Elsevier, vol. 97(C), pages 93-110.
    20. Arthur Pewsey & Toshihiro Abe, 2015. "The sinh-arcsinhed logistic family of distributions: properties and inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 573-594, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:23:y:2014:i:4:p:751-768. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.