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Data-Driven Rate-Optimal Specification Testing In Regression Models

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Author Info
Emmanuel Guerre (LSTA-Université Paris 6)
Pascal Lavergne (University of Toulouse—GREMAQ & INRA)

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Abstract

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/\sqrt{n}. Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.

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File URL: http://129.3.20.41/eps/em/papers/0411/0411008.pdf
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Publisher Info
Paper provided by EconWPA in its series Econometrics with number 0411008.

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Length: 30 pages
Date of creation: 12 Nov 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0411008

Note: Type of Document - pdf; pages: 30. Forthcoming in the Annals of Statistics
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Web page: http://129.3.20.41

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Related research
Keywords: Hypothesis testing; nonparametric adaptive tests; selection methods;

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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References listed on IDEAS
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, 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!]
  2. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society. [Downloadable!]
  3. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1139-1171, October. [Downloadable!]
  6. O. V. Lepskii & E. Mammen & V. G. Spokoiny, . "Optimal Spatial Adaptation to Inhomogeneous Smoothness: an Approach Based on Kernel Estimates with Variable Bandwidth Selectors," Sonderforschungsbereich 373 1995-3, Humboldt Universitaet Berlin.
  7. Gozalo, Pedro L., 1997. "Nonparametric bootstrap analysis with applications to demographic effects in demand functions," Journal of Econometrics, Elsevier, vol. 81(2), pages 357-393, December. [Downloadable!] (restricted)
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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. 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!]
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