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Minimax Rates for Nonparametric Specification Testing in Regression Models

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Author Info
E. Guerre (Universite Paris 6 and CREST)
Pascal Lavergne (INRA-ESR)

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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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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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June. [Downloadable!] (restricted)
  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. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Joel Horowitz & Sokbae 'Simon' Lee, 2007. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," CeMMAP working papers CWP02/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  2. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, EconWPA. [Downloadable!]
  3. 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. [Downloadable!]
  4. Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltà di Scienze economiche dell'Università di Lugano 0803, Biblioteca universitaria di Lugano (University Library of Lugano). [Downloadable!]
  5. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM. [Downloadable!]
  6. Richard Blundell & Joel Horowitz, 2004. "A nonparametric test of exogeneity," CeMMAP working papers CWP15/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  7. 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. [Downloadable!]
  8. Emmanuel Guerre & Pascal Lavergne, 2001. "Rate-optimal data-driven specification testing in regression models," Econometrics 0107001, EconWPA. [Downloadable!]
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