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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)

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://128.118.178.162/eps/em/papers/0411/0411008.pdf
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Bibliographic 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://128.118.178.162

Related research

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

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References

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  1. 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.
  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.
  3. 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.
  4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  5. 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.
  6. 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.
  7. 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.
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Cited by:
  1. 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.

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