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Bandwidth choice for differentiation

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  • Rice, John A.

Abstract

We propose a class of procedures for choosing the bandwidth, or smoothing parameter, for linear nonparametric estimates of the rth derivative of a smooth function observed with error on a discrete set of points. These procedures are based on minimizing a nearly unbiased estimate of the integrated mean square error. Theoretical justification is provided in the special case of a tapered Fourier series estimate.

Suggested Citation

  • Rice, John A., 1986. "Bandwidth choice for differentiation," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 251-264, August.
    • Handle: RePEc:eee:jmvana:v:19:y:1986:i:2:p:251-264
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    Cited by:

    1. Li, Cong & Wang, Yanfei, 2016. "Gradient-based bandwidth selection for estimating average derivatives," Economics Letters, Elsevier, vol. 140(C), pages 19-22.
    2. Salim Bouzebda & Mohamed Chaouch & Sultana Didi Biha, 2022. "Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 737-771, August.
    3. Xie, Qichang & Sun, Qiankun, 2019. "Computation and application of robust data-driven bandwidth selection for gradient function estimation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 274-293.
    4. Juei-Chao Chen, 1994. "Testing for no effect in nonparametric regression via spline smoothing techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 251-265, June.
    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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