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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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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
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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

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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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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. 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)
  3. 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.
  4. 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)
  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, July. [Downloadable!]
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