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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

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.

Suggested Citation

  • Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:3:p:947-962
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00518.x
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    Citations

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    Cited by:

    1. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    2. 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.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Klein, Roger & Shen, Chan & Vella, Francis, 2015. "Estimation of marginal effects in semiparametric selection models with binary outcomes," Journal of Econometrics, Elsevier, vol. 185(1), pages 82-94.
    5. Michael Jansson & Demian Pouzo, 2017. "Some Large Sample Results for the Method of Regularized Estimators," Papers 1712.07248, arXiv.org.
    6. 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.
    7. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2014. "Small Bandwidth Asymptotics For Density-Weighted Average Derivatives," Econometric Theory, Cambridge University Press, vol. 30(01), pages 176-200, February.
    8. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    9. 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.
    10. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Dec 2017.
    11. Hidehiko Ichimura & Whitney K. Newey, 2015. "The Influence Function of Semiparametric Estimators," CIRJE F-Series CIRJE-F-985, CIRJE, Faculty of Economics, University of Tokyo.
    12. Chan Shen & Roger Klein, 2017. "Recursive Differencing: Bias Reduction with Regular Kernels," Departmental Working Papers 201701, Rutgers University, Department of Economics.
    13. Rothe, Christoph & Firpo, Sergio Pinheiro, 2013. "Semiparametric estimation and inference using doubly robust moment conditions," Textos para discussão 330, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    14. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    15. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey, 2016. "Locally robust semiparametric estimation," CeMMAP working papers CWP31/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Roger Klein & Chan Shen & Francis Vella, 2011. "Semiparametric selection models with binary outcomes," CeMMAP working papers CWP30/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Dennis Kristensen & Bernard Salanié, 2010. "Higher Order Improvements for Approximate Estimators," CAM Working Papers 2010-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    18. Robins, James M. & Li, Lingling & Tchetgen, Eric Tchetgen & van der Vaart, Aad, 2016. "Asymptotic normality of quadratic estimators," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3733-3759.
    19. Whitney K. Newey & James M. Robins, 2017. "Cross-fitting and fast remainder rates for semiparametric estimation," CeMMAP working papers CWP41/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    21. Lee, Jiyon, 2015. "A semiparametric single index model with heterogeneous impacts on an unobserved variable," Journal of Econometrics, Elsevier, vol. 184(1), pages 13-36.
    22. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Robust Kernel Estimator For Densities Of Unknown," Departmental Working Papers 2005-05, McGill University, Department of Economics.

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