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Testing for Symmetry and Conditional Symmetry Using Asymmetric Kernels

Author

Listed:
  • Marcelo FERNANDES

    (University of London)

  • Eduardo F. MENDES

    (Northwestern University)

  • Olivier SCAILLET

    (University of Geneva and Swiss Finance Institute)

Abstract

We derive nonparametric tests of symmetry using asymmetric kernels with either shrinking or fixed bandwidths. We show how to extend the approach to examine conditional symmetry by deriving conditions under which our tests are applicable to residuals from semiparametric models with a (sufficiently smooth) nonparametric link function. As a by-product, we prove the consistency of the asymmetric kernel estimator of the derivative of the density function. Simulations show that the asymptotic tests perform well even in very small samples, entailing better size and power properties than some of the existing symmetry tests.

Suggested Citation

  • Marcelo FERNANDES & Eduardo F. MENDES & Olivier SCAILLET, "undated". "Testing for Symmetry and Conditional Symmetry Using Asymmetric Kernels," Swiss Finance Institute Research Paper Series 11-32, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp1132
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    2. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-27, June.

    More about this item

    Keywords

    asymmetric kernel; gamma kernel; inverse Gaussian kernel; nonparametric testing; reciprocal inverse Gaussian kernel; symmetry.;

    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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