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Bootstrapping Semiparametric Models with Single-Index Nuisance Parameters, Second Version

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  • Kyungchul Song

    ()
    (Department of Economics, University of Pennsylvania)

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    Abstract

    This 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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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/10-026.pdf
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    Bibliographic Info

    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 10-026.

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    Length: 51 pages
    Date of creation: 16 Oct 2009
    Date of revision: 02 Aug 2010
    Handle: RePEc:pen:papers:10-026

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    Related research

    Keywords: semiparametric conditional moment restrictions; single-index restrictions; cube root asymptotics; bootstrap;

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    1. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
    2. Hardle, W.K. & Tsybakov, A.B., 1992. "How sensitive are average derivatives?," Discussion Paper 1992-8, Tilburg University, Center for Economic Research.
    3. 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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