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Local Polynomial Derivative Estimation: Analytic or Taylor?

In: Essays in Honor of Aman Ullah

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  • Jeffrey S. Racine

Abstract

Local polynomial regression is extremely popular in applied settings. Recent developments in shape-constrained nonparametric regression allow practitioners to impose constraints on local polynomial estimators thereby ensuring that the resulting estimates are consistent with underlying theory. However, it turns out that local polynomial derivative estimates may fail to coincide with the analytic derivative of the local polynomial regression estimate which can be problematic, particularly in the context of shape-constrained estimation. In such cases, practitioners might prefer to instead use analytic derivatives along the lines of those proposed in the local constant setting by Rilstone and Ullah (1989). Demonstrations and applications are considered.

Suggested Citation

  • Jeffrey S. Racine, 2016. "Local Polynomial Derivative Estimation: Analytic or Taylor?," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 617-633, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320160000036027
    DOI: 10.1108/S0731-905320160000036027
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    Cited by:

    1. 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.
    2. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).

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    JEL classification:

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

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