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A Bootstrap Test for Single Index Models


Author Info

  • Wolfgang Haerdle

    (Humboldt-University of Berlin)

  • Enno MAMMEN

    (Ruprecht-Karls-University Heidelberg)

  • Isabel Proenca



Single index models are frequently used in econometrics and biometrics. Logit and Probit models are special cases with fixed link functions. In this paper we consider a bootstrap specification test that detects nonparametric deviations of the link function. The bootstrap is used with the aim to find a more accurate distribution under the null than the normal approximation. We prove that the statistic and its bootstrapped version have the same asymptotic distribution. In a simulation study we show that the bootstrap is able to capture the negative bias and the skewness of the test statistic. It yields better approximations to the true critical values and consequently it has a more accurate level and superior power properties. We propose a modification of the HH statistic which reduces considerably the dependency of the test performance on the bandwidth choice. We show that the bootstrap of this modified statistic works as well.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0508007.

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Length: 28 pages
Date of creation: 05 Aug 2005
Date of revision:
Handle: RePEc:wpa:wuwpem:0508007

Note: Type of Document - pdf; prepared on windows; pages: 28
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Keywords: Bootstrap; kernel estimate; single index model; specification test.;

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Cited by:
  1. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2001. "Bootstrap Inference in Semiparametric Generalized Additive Models," Finance Working Papers 01-3, University of Aarhus, Aarhus School of Business, Department of Business Studies.


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