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Rate-optimal data-driven specification testing in regression models

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Author Info

  • Emmanuel Guerre

    (LSTA, Université Paris 6)

  • Pascal Lavergne

    (INRA-ESR Toulouse)

Abstract

We propose a general procedure for testing that a regression function has a prescribed parametric form. We allow for multivariate regressors, non-normal errors and heteroscedasticity of unknown form. The test relies upon a nonparametric linear estimation method, such as a sieves expansion or the kernel method. The choice of the smoothing parameter is data-driven. Under the null hypothesis, the asymptotic distribution of the test statistic is the standard normal distribution. Use of bootstrap critical values is formally justified. The test is shown to be adaptive and rate-optimal in the minimax sense. Detection of Pitman-type local alternatives is also studied.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0107001.

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Date of creation: 12 Jul 2001
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Handle: RePEc:wpa:wuwpem:0107001

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Web page: http://128.118.178.162

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Keywords: rate-optimal nonparametric data-driven specification test;

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References

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  1. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
  3. Ellison, Glenn & Ellison, Sara Fisher, 2000. "A simple framework for nonparametric specification testing," Journal of Econometrics, Elsevier, vol. 96(1), pages 1-23, May.
  4. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
  5. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  6. Chen, Juei-Chao, 1994. "Testing goodness of fit of polynomial models via spline smoothing techniques," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 65-76, January.
  7. Joel Horowitz, 2000. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Econometric Society World Congress 2000 Contributed Papers 0166, Econometric Society.
  8. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
  9. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  10. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  11. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  12. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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Cited by:
  1. Juan M. Rodríguez-Póo & Stefan Sperlich & Philippe Vieu, 2012. "A Practical Test for Misspecification in Regression: Functional Form, Separability and Distribution," Research Papers by the Department of Economics, University of Geneva 12093, Département des Sciences Économiques, Université de Genève.

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