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Data-Driven Rate-Optimal Specification Testing In Regression Models

  • Emmanuel Guerre

    (LSTA-Université Paris 6)

  • Pascal Lavergne

    (University of Toulouse—GREMAQ & INRA)

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://econwpa.repec.org/eps/em/papers/0411/0411008.pdf
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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
Contact details of provider: Web page: http://econwpa.repec.org

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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. 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.
  3. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  4. 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.
  5. 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.
  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. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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