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Specification Tests for the Distribution of Errors in Nonoarametric Regression: A Martingale Approach

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Author Info

  • Alicia Pérez Alonso

    ()
    (Universidad de Alicante)

  • Juan Mora

    ()
    (Universidad de Alicante)

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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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2008-11.pdf
File Function: Fisrt version / Primera version, 2008
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2008-11.

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Length: 36 pages
Date of creation: Jun 2008
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2008-11

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Related research

Keywords: Specification Tests; Nonparametric Regression; Empirical Processes.;

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References

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  1. Juan Mora, 2005. "The Two-Sample Problem With Regression Errors: An Empirical Process Approach," Working Papers. Serie AD 2005-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
  3. Michael G. Akritas, 2001. "Non-parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567.
  4. 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.
  5. 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.
  6. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
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Citations

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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, 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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