IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v71y2005i4p323-335.html
   My bibliography  Save this article

Chebyshev-type inequalities for scale mixtures

Author

Listed:
  • Csiszar, Villo
  • Móri, Tamás F.
  • Székely, Gábor J.

Abstract

For important classes of symmetrically distributed random variables X the smallest constants C[alpha] are computed on the right-hand side of Chebyshev's inequality P(X[greater-or-equal, slanted]t)[less-than-or-equals, slant]C[alpha]EX[alpha]/t[alpha]. For example if the distribution of X is a scale mixture of centered normal random variables, then the smallest C2=0.331... and, as [alpha]-->[infinity], the smallest C[alpha][downwards arrow]0 and .

Suggested Citation

  • Csiszar, Villo & Móri, Tamás F. & Székely, Gábor J., 2005. "Chebyshev-type inequalities for scale mixtures," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 323-335, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:323-335
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00004-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Thomas Sellke, 1996. "Generalized gauss-chebyshev inequalities for unimodal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 107-121, December.
    2. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
    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. Adell, José A. & Lekuona, Alberto, 2006. "Every random variable satisfies a certain nontrivial integrability condition," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1603-1606, 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. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    2. Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    3. Polonik, Wolfgang & Yao, Qiwei, 2008. "Testing for multivariate volatility functions using minimum volume sets and inverse regression," Journal of Econometrics, Elsevier, vol. 147(1), pages 151-162, November.
    4. Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2008. "Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00270719, HAL.
    5. Buckley, Ian & Saunders, David & Seco, Luis, 2008. "Portfolio optimization when asset returns have the Gaussian mixture distribution," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1434-1461, March.
    6. González-Pedraz, Carlos & Moreno, Manuel & Peña, Juan Ignacio, 2014. "Tail risk in energy portfolios," Energy Economics, Elsevier, vol. 46(C), pages 422-434.
    7. Shuangzhe Liu & Chris Heyde & Wing-Keung Wong, 2011. "Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models," Statistical Papers, Springer, vol. 52(3), pages 621-632, August.
    8. Dipierro, Serena & Valdinoci, Enrico, 2021. "Description of an ecological niche for a mixed local/nonlocal dispersal: An evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 575(C).
    9. Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    10. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
    11. Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2010. "BL-GARCH model with elliptical distributed innovations," Post-Print halshs-00368340, HAL.
    12. Szulga, Jerzy, 2009. "On selfdecomposable Stieltjes transforms," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 748-752, March.
    13. Abel Elizalde, 2006. "Credit Risk Models I: Default Correlation in Intensity Models," Working Papers wp2006_0605, CEMFI.
    14. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    15. Packham, Natalie & Kalkbrener, Michael & Overbeck, Ludger, 2014. "Default probabilities and default correlations under stress," Frankfurt School - Working Paper Series 211, Frankfurt School of Finance and Management.
    16. Shuangzhe Liu & Chris Heyde, 2008. "On estimation in conditional heteroskedastic time series models under non-normal distributions," Statistical Papers, Springer, vol. 49(3), pages 455-469, July.
    17. Jeroen Rombouts & Marno Verbeek, 2009. "Evaluating portfolio Value-at-Risk using semi-parametric GARCH models," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 737-745.
    18. Hosseini, Reshad & Sra, Suvrit & Theis, Lucas & Bethge, Matthias, 2016. "Inference and mixture modeling with the Elliptical Gamma Distribution," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 29-43.
    19. Carol Alexander & Andrew Scourse, 2004. "Bivariate normal mixture spread option valuation," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 637-648.
    20. Abel Elizalde, 2006. "Credit Risk Models II: Structural Models," Working Papers wp2006_0606, CEMFI.

    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:eee:stapro:v:71:y:2005:i:4:p:323-335. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.