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A Bootstrap Test for Single Index Models

Author

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  • HÄRDLE, Wolfgang

    (Institut für Statistik und Ökonometrice, Wirtschaftswissenschaftliche Fakultät, Humboldt Universität zu Berlin)

  • DIAS PROENCA, sabel M.

    (CORE and Institut de Statistique, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

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 specification test that detects nonparametric deviations of the link function, e. g., testing against a semiparametric alternative. Simulations with single index models have shown that the empirical power of this test may be affected in small samples. In this work the bootstrap is used with the aim to find a more accurate distribution under the null than the standard normal. We prove that the statistic and its bootstrapped version have the same asymptotic distribution. A simulation study is performed to investigate the empirical behaviour of this approach. The bootstrapped critical values yield better approximations to the true values.

Suggested Citation

  • HÄRDLE, Wolfgang & DIAS PROENCA, sabel M., 1993. "A Bootstrap Test for Single Index Models," LIDAM Discussion Papers CORE 1993025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1993025
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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. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 265-300, April.

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    More about this item

    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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