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A Bootstrap Test for Single Index Models


Author Info

  • 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)


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.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1993025.

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Date of creation: 01 Jun 1993
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Handle: RePEc:cor:louvco:1993025

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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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