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Minimax Rates for Nonparametric Specification Testing in Regression Models

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  • 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.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0644.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0644

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  1. Joel Horowitz, 2000. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0166, Econometric Society.
  2. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, Elsevier, vol. 17(3), pages 199-204, June.
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Cited by:
  1. Horowitz, Joel L. & Spokoiny, Vladimir G., 2000. "An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models," Working Papers, University of Iowa, Department of Economics 00-04, University of Iowa, Department of Economics.
  2. 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, Elsevier, vol. 152(2), pages 141-152, October.
  3. Richard Blundell & Joel Horowitz, 2004. "A nonparametric test of exogeneity," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP15/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Emmanuel Guerre & Pascal Lavergne, 2001. "Rate-optimal data-driven specification testing in regression models," Econometrics, EconWPA 0107001, EconWPA.
  5. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers, Centro de Investigacion Economica, ITAM 0101, Centro de Investigacion Economica, ITAM.
  6. 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.
  7. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics, EconWPA 0411008, EconWPA.
  8. Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltà di Scienze economiche dell'Università di Lugano, USI Università della Svizzera italiana 0803, USI Università della Svizzera italiana.

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