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Minimax Rates for Nonparametric Specification Testing in Regression Models

Author

Listed:
  • E. Guerre

    (Universite Paris 6 and CREST)

  • Pascal Lavergne

    (INRA-ESR)

Abstract

We deal with the issue of testing the specification of a regression function. As a leading case, we consider testing for a pure noise model. We study the smallest local alternatives that can be detected asymptotically in a minimax sense. We propose a simple testing procedure that has asymptotic optimal minimax properties for regular alternatives. We then adapt this procedure to testing the specification of a nonlinear parametric regression model. As a by-product, we obtain the rate of the optimal smoothing parameter that ensures optimal minimax properties for the test. We show that, by contrast, non-smoothing tests, such as Bierens' (1982) integrated conditional moment test, have undesirable minimax properties.

Suggested Citation

  • E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  • Handle: RePEc:ecm:wc2000:0644
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    References listed on IDEAS

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    1. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    2. 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.
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    Cited by:

    1. Horowitz, Joel L. & Lee, Sokbae, 2009. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," Journal of Econometrics, Elsevier, vol. 152(2), pages 141-152, October.
    2. Juan Carlos Escanciano & Kyungchul Song, 2007. "Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects," PIER Working Paper Archive 07-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltà di Scienze economiche dell'Università di Lugano 0803, USI Università della Svizzera italiana.
    4. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    5. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1035-1058.
    6. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, EconWPA.
    7. Horowitz, Joel L. & Spokoiny, Vladimir G., 2000. "An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models," Working Papers 00-04, University of Iowa, Department of Economics.
    8. Emmanuel Guerre & Pascal Lavergne, 2001. "Rate-optimal data-driven specification testing in regression models," Econometrics 0107001, EconWPA.
    9. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.

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