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A Bootstrap Test for Single Index Models

  • Wolfgang Haerdle

    (Humboldt-University of Berlin)

  • Enno MAMMEN

    (Ruprecht-Karls-University Heidelberg)

  • Isabel Proenca

    (ISEG-UTL)

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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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
Contact details of provider: Web page: http://econwpa.repec.org

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