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Twicing Kernels and a Small Bias Property of Semiparametric Estimators

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  • Whitney K. Newey
  • Fushing Hsieh
  • James M. Robins
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    Abstract

    The purpose of this note is to show how semiparametric estimators with a small bias property can be constructed. The small bias property (SBP) of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based. We show that semiparametric estimators based on twicing kernels have the SBP. We also show that semiparametric estimators where nonparametric kernel estimation does not affect the asymptotic variance have the SBP. In addition we discuss an interpretation of series and sieve estimators as idempotent transformations of the empirical distribution that helps explain the known result that they lead to the SBP. In Monte Carlo experiments we find that estimators with the SBP have mean-square error that is smaller and less sensitive to bandwidth than those that do not have the SBP. Copyright The Econometric Society 2004.

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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00518.x
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    Bibliographic Info

    Article provided by Econometric Society in its journal Econometrica.

    Volume (Year): 72 (2004)
    Issue (Month): 3 (05)
    Pages: 947-962

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    Handle: RePEc:ecm:emetrp:v:72:y:2004:i:3:p:947-962

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    Cited by:
    1. Xiaohong Chen & Demian Pouzo, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP20/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Dennis Kristensen & Bernard Salanie, 2010. "Higher Order Improvements for Approximate Estimators," Discussion Papers 0910-15, Columbia University, Department of Economics.
    3. Klein, Roger & Vella, Francis, 2010. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," Journal of Econometrics, Elsevier, vol. 154(2), pages 154-164, February.
    4. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2010. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1070-1083.
    5. Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2008. "Small Bandwidth Asymptotics for Density-Weighted Average Derivatives," CREATES Research Papers 2008-24, School of Economics and Management, University of Aarhus.
    6. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    7. Xiaohong Chen & Demian Pouzo, 2008. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP09/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Xiaohong Chen & Demian Pouzo, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Cowles Foundation Discussion Papers 1640R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2009.
    9. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Robust Kernel Estimator For Densities Of Unknown," Departmental Working Papers 2005-05, McGill University, Department of Economics.
    10. Klein, Roger & Shen, Chan & Vella, Francis, 2011. "Semiparametric Selection Models with Binary Outcomes," IZA Discussion Papers 6008, Institute for the Study of Labor (IZA).
    11. Chen, Xiaohong & Pouzo, Demian, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Working Papers 38, Yale University, Department of Economics.

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