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Rate-optimal data-driven specification testing in regression models

Author

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  • 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, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0107001
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    References listed on IDEAS

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    5. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    6. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    7. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    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.
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    12. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
    13. 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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    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.

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    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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