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A Bootstrap Test for Single Index Models

Author

Listed:
  • Wolfgang Haerdle

    (Humboldt-University of Berlin)

  • Enno MAMMEN

    (Ruprecht-Karls-University Heidelberg)

  • Isabel Proenca

    (ISEG-UTL)

Abstract

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.

Suggested Citation

  • Wolfgang Haerdle & Enno MAMMEN & Isabel Proenca, 2005. "A Bootstrap Test for Single Index Models," Econometrics 0508007, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0508007
    Note: Type of Document - pdf; prepared on windows; pages: 28
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0508/0508007.pdf
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    References listed on IDEAS

    as
    1. Isabel Proenca, "undated". "On the performance of the H-H Test," Statistic und Oekonometrie 9310, Humboldt Universitaet Berlin.
    2. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July.
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    Cited by:

    1. Alan Ker & A. Tolga Ergun, 2007. "On the Revelation of Private Information in the U.S. Crop Insurance Program," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(4), pages 761-776.
    2. H rdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 265-300, April.

    More about this item

    Keywords

    Bootstrap; kernel estimate; single index model; specification test.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: 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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