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Recursive Differencing: Bias Reduction with Regular Kernels

Author

Listed:
  • Chan Shen

    () (University of Texas MD Anderson Cancer Center)

  • Roger Klein

    () (Rutgers University)

Abstract

It is well known that it is important to control the bias in estimating conditional expectations in order to obtain asymptotic normality for quantities of interest (e.g. a finite dimensional parameter vector in semiparametric models or averages of marginal effects in the nonparametric case). For this purposes, higher order kernel methods are often employed in developing the theory. However such methods typically do not perform well at moderate sample sizes. Moreover, and perhaps related to their performance, non-optimal windows are selected with undersmoothing needed to ensure the appropriate bias order. We propose a recursive differencing approach to bias reduction for a nonparametric estimator of a conditional expectation, where the order of the bias depending on the stage of the recursion. It performs much better at moderate sample sizes than regular or higher order kernels while retaining a bias of any desired order and a convergence rate the same as that of higher order kernels. We also propose an approach to implement this estimator under optimal windows, which ensures asymptotic normality in semiparametric multiple index models of arbitrary dimension. This mechanism further contributes to its very good finite sample performance.

Suggested Citation

  • Chan Shen & Roger Klein, 2017. "Recursive Differencing: Bias Reduction with Regular Kernels," Departmental Working Papers 201701, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201701
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    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2017-01.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    3. Klein, Roger & Shen, Chan, 2010. "Bias Corrections In Testing And Estimating Semiparametric, Single Index Models," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1683-1718, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bias Reduction; Nonparametric Expectations; Semiparametric Models;

    JEL classification:

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

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