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Goodness of fit test for discrete random variables

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  • Lee, Sangyeol

Abstract

In this paper, a goodness of fit (gof) test for discrete random variables is studied. For the test, the empirical process gof test constructed based on the Khmaladze transformation method is considered to remove the parameter estimation effect. Further, the approach of the continuous extension of discrete random variables introduced in Denuit and Lambert (2005) is adopted. It is shown that under regularity conditions, the transformed empirical process weakly converges to a standard Brownian motion. As a gof test based on this result, the maximum entropy type test designed by Lee et al. (2011) is considered. As with the empirical process gof test, Vasicek’s entropy test is also considered and a properly modified version, whose limiting distribution is unaffected by the choice of parameter estimates, is provided. Simulation results are provided for illustration.

Suggested Citation

  • Lee, Sangyeol, 2014. "Goodness of fit test for discrete random variables," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 92-100.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:92-100
    DOI: 10.1016/j.csda.2013.07.026
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    References listed on IDEAS

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    1. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    2. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    3. Lee, Sangyeol & Vonta, Ilia & Karagrigoriou, Alex, 2011. "A maximum entropy type test of fit," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2635-2643, September.
    4. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
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    Cited by:

    1. Kheifets, Igor & Velasco, Carlos, 2017. "New goodness-of-fit diagnostics for conditional discrete response models," Journal of Econometrics, Elsevier, vol. 200(1), pages 135-149.

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