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Specification tests for the distribution of errors in nonparametric regression: a martingale approach

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  • Juan Mora
  • Alicia Pérez-Alonso

Abstract

We discuss how to test whether the distribution of regression errors belongs to a parametric family of continuous distribution functions, making no parametric assumption about the conditional mean or the conditional variance in the regression model. We propose using test statistics that are based on a martingale transform of the estimated empirical process. We prove that these statistics are asymptotically distribution-free, and two Monte Carlo experiments show that they work reasonably well in practice.

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  • Juan Mora & Alicia Pérez-Alonso, 2009. "Specification tests for the distribution of errors in nonparametric regression: a martingale approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 441-452.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:441-452
    DOI: 10.1080/10485250802666192
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    1. Kloek, Teun & van Dijk, Herman K., 1978. "Efficient estimation of income distribution parameters," Journal of Econometrics, Elsevier, vol. 8(1), pages 61-74, August.
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    3. Koul, Hira L. & Sakhanenko, Lyudmila, 2005. "Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 290-302, October.
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    5. McDonald, James B. & Butler, Richard J., 1990. "Regression models for positive random variables," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 227-251.
    6. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    7. 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.
    8. Müller Ursula U. & Schick Anton & Wefelmeyer Wolfgang, 2007. "Estimating the error distribution function in semiparametric regression," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-18, January.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Heuchenne, Cédric & Van Keilegom, Ingrid, 2010. "Goodness-of-fit tests for the error distribution in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1942-1951, August.

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