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Rate-optimal data-driven specification testing in regression models

Author

Listed:
  • 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.

Suggested Citation

  • Emmanuel Guerre & Pascal Lavergne, 2001. "Rate-optimal data-driven specification testing in regression models," Econometrics 0107001, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0107001
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    References listed on IDEAS

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    1. 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.
    2. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    3. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    4. Ellison, Glenn & Ellison, Sara Fisher, 2000. "A simple framework for nonparametric specification testing," Journal of Econometrics, Elsevier, vol. 96(1), pages 1-23, May.
    5. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    6. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    7. 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.
    8. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    9. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    10. 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.
    11. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
    12. 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.
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    Citations

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    Cited by:

    1. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2278-2294, December.
    2. 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 Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 12093, Institut d'Economie et Econométrie, Université de Genève.

    More about this item

    Keywords

    rate-optimal nonparametric data-driven specification test;

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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