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Testing for Bivariate Spherical Symmetry

Author

Listed:
  • Einmahl, J.H.J.

    (Tilburg University, Center For Economic Research)

  • Gantner, M.

    (Tilburg University, Center For Economic Research)

Abstract

An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic ones, are presented. In a simulation study, the good perfor- mance of the test is demonstrated. Furthermore, a real data example is presented.
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Suggested Citation

  • Einmahl, J.H.J. & Gantner, M., 2010. "Testing for Bivariate Spherical Symmetry," Discussion Paper 2010-71, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:b50b8093-4f4c-4afa-af04-3c477087aca7
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    References listed on IDEAS

    as
    1. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    2. Jiajuan Liang & Kai-Tai Fang & Fred Hickernell, 2008. "Some necessary uniform tests for spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 679-696, September.
    3. Einmahl, J.H.J., 1987. "Multivariate empirical processes," Other publications TiSEM 4d74fa6b-5281-48ea-aa4d-5, Tilburg University, School of Economics and Management.
    4. Koltchinskii, V. I. & Li, Lang, 1998. "Testing for Spherical Symmetry of a Multivariate Distribution," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 228-244, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.

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    More about this item

    Keywords

    Asymptotic distribution; distribution-free; empirical like- lihood; hypothesis test; spherical symmetry.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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