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Gradient-based bandwidth selection for estimating average derivatives

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  • Li, Cong
  • Wang, Yanfei

Abstract

In this paper, we propose to estimate average derivatives of a function by averaging the sample pointwise local linear derivatives with the bandwidth being selected optimally. Our estimator has better finite sample performance than that of Li, Lu & Ullah (2003) because our pointwise derivative estimate reaches the optimal convergence rate. Simulations confirm our theoretical analysis.

Suggested Citation

  • Li, Cong & Wang, Yanfei, 2016. "Gradient-based bandwidth selection for estimating average derivatives," Economics Letters, Elsevier, vol. 140(C), pages 19-22.
    • Handle: RePEc:eee:ecolet:v:140:y:2016:i:c:p:19-22
    DOI: 10.1016/j.econlet.2015.12.005
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    References listed on IDEAS

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    1. Rilstone, Paul, 1991. "Nonparametric Hypothesis Testing with Parametric Rates of Convergence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(1), pages 209-227, February.
    2. Rice, John A., 1986. "Bandwidth choice for differentiation," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 251-264, August.
    3. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-1223, September.
    4. Li, Dong & Li, Qi, 2010. "Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters," Journal of Econometrics, Elsevier, vol. 157(1), pages 179-190, July.
    5. Henderson, Daniel J. & Li, Qi & Parmeter, Christopher F. & Yao, Shuang, 2015. "Gradient-based smoothing parameter selection for nonparametric regression estimation," Journal of Econometrics, Elsevier, vol. 184(2), pages 233-241.
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    More about this item

    Keywords

    Average derivatives estimation; Kernel smoothing; Optimal bandwidth selection;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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