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The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives

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  • Yoshihiko Nishiyama
  • Peter M. Robinson

Abstract

In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the error in the normal approximation, so that refined approximations are of interest, especially in sample sizes that are not enormous. We show that a bootstrap distribution achieves a valid Edgeworth correction in the case of density-weighted averaged derivative estimates of semiparametric index models. Approaches to bias reduction are discussed. We also develop a higher-order expansion to show that the bootstrap achieves a further reduction in size distortion in the case of two-sided testing. The finite-sample performance of the methods is investigated by means of Monte Carlo simulations from a Tobit model. Copyright The Econometric Society 2005.

Suggested Citation

  • 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.
    • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:3:p:903-948
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00598.x
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    Cited by:

    1. Cattaneo, Matias D. & Farrell, Max H. & Jansson, Michael & Masini, Ricardo P., 2025. "Higher-order refinements of small bandwidth asymptotics for density-weighted average derivative estimators," Journal of Econometrics, Elsevier, vol. 252(PB).
    2. Marcia M Schafgans & Victoria Zinde-Walshyz, 2008. "Smoothness Adaptive AverageDerivative Estimation," STICERD - Econometrics Paper Series 529, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. 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.
    4. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    5. repec:hum:wpaper:sfb649dp2009-028 is not listed on IDEAS
    6. Victoria Zinde-Walsh & Marcia M.A. Schafgans, 2007. "Robust Average Derivative Estimation," Departmental Working Papers 2007-12, McGill University, Department of Economics.
    7. Xia, Yingcun & Härdle, Wolfgang Karl & Linton, Oliver, 2009. "Optimal smoothing for a computationally and statistically efficient single index estimator," SFB 649 Discussion Papers 2009-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    9. Subbotin, Viktor, 2008. "Essays on the econometric theory of rank regressions," MPRA Paper 14086, University Library of Munich, Germany.
    10. Chuan Goh, 2009. "Bootstrap-based Bandwidth Selection for Semiparametric Generalized Regression Estimators," Working Papers tecipa-375, University of Toronto, Department of Economics.
    11. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2014. "Small Bandwidth Asymptotics For Density-Weighted Average Derivatives," Econometric Theory, Cambridge University Press, vol. 30(1), pages 176-200, February.
    12. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    13. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    14. Subbotin, Viktor, 2007. "Asymptotic and bootstrap properties of rank regressions," MPRA Paper 9030, University Library of Munich, Germany, revised 20 Mar 2008.
    15. Gao, Jiti & Gijbels, Irene, 2005. "Bandwidth selection for nonparametric kernel testing," MPRA Paper 11982, University Library of Munich, Germany, revised Jun 2007.
    16. Nishiyama, Y., 2004. "Minimum normal approximation error bandwidth selection for averaged derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(1), pages 53-61.
    17. Christopher Withers & Saralees Nadarajah, 2013. "Density estimates of low bias," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 357-379, April.

    More about this item

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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