A Bootstrap Test for Single Index Models
AbstractSingle 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 InfoPaper provided by EconWPA in its series Econometrics with number 0508007.
Length: 28 pages
Date of creation: 05 Aug 2005
Date of revision:
Note: Type of Document - pdf; prepared on windows; pages: 28
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Bootstrap; kernel estimate; single index model; specification test.;
Other versions of this item:
- Härdle, Wolfgang & Mammen, Enno & Proença, Isabel, 2000. "A bootstrap test for single index models," SFB 373 Discussion Papers 2000,20, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- HÄRDLE, Wolfgang & DIAS PROENCA, sabel M., 1993. "A Bootstrap Test for Single Index Models," CORE Discussion Papers 1993025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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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- 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.
- 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.
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