Bootstrapping Semiparametric Models with Single-Index Nuisance Parameters, Second Version
AbstractThis paper considers models of conditional moment restrictions that involve non-parametric functions of single-index nuisance parameters. This paper proposes a bootstrap method of constructing confidence sets which has the following three merits. First, the bootstrap is valid even when the single-index estimator follows cube-root asymptotics. Second, the bootstrap method accommodates conditional heteroskedasticity. Third, the bootstrap does not require re-estimation of the single-index component for each bootstrap sample. The method is built on this paper’s general finding that as far as the single-index is a conditioning variable of a conditional expectation, the influence of the estimated single-indices in these models is asymptotically negligible. This finding is shown to have a generic nature through an analysis of Fréchet derivatives of linear functionals of conditional expectations. Some results from Monte Carlo simulations are presented and discussed.
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Bibliographic InfoPaper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 10-026.
Length: 51 pages
Date of creation: 16 Oct 2009
Date of revision: 02 Aug 2010
semiparametric conditional moment restrictions; single-index restrictions; cube root asymptotics; bootstrap;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
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- Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
- Hardle, Wolfgang & Tsybakov, A. B., 1993.
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- Hardle, W. & Tsybakov, A.B., 1992. "How Sensitive are Average Derivatives?," Papers 9208, Tilburg - Center for Economic Research.
- Hardle, W. & Tsybakov, A., 1991. "How sensitive are average derivates ?," CORE Discussion Papers 1991044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
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