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Bootstrap-based Bandwidth Selection for Semiparametric Generalized Regression Estimators

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  • Chuan Goh

Abstract

This paper considers the problem of implementing semiparametric extremum estimators of a generalized regression model with an unknown link function. The class of estimator under consideration includes as special cases the semiparametric least-squares estimator of Ichimura (1993) as well as the semiparametric quasi-likelihood estimator of Klein and Spady (1993). In general, it is assumed to involve the computation of a nonparametric kernel estimate of the link function that appears in place of the true, but unknown, link function in the appropriate location in a smooth criterion function. The specific question considered in this paper concerns the practical selection of the degree of smoothing to be used in computing the nonparametric regression estimate. This paper proposes a method for selecting the smoothing parameter via resampling. The particular method suggested here involves using a resample of smaller size than the original sample. Specific guidance on selecting the resample size is given, and simulation evidence is presented to illustrate the utility of this method for samples of moderate size.

Suggested Citation

  • Chuan Goh, 2009. "Bootstrap-based Bandwidth Selection for Semiparametric Generalized Regression Estimators," Working Papers tecipa-375, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-375
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    References listed on IDEAS

    as
    1. Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, May.
    2. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
    3. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    4. Yingcun Xia & Wolfgang Härdle & Oliver Linton, 2009. "Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator," SFB 649 Discussion Papers SFB649DP2009-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 372-395, June.
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    More about this item

    Keywords

    Bandwidth selection; semiparametric; single-index model; bootstrap; m-out-of-n bootstrap; kernel smoothing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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