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Local Polynomial Derivative Estimation: Analytic or Taylor?

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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 & Ullah (1989). Demonstrations and applications are considered.

Suggested Citation

  • Jeffrey S. Racine, 2015. "Local Polynomial Derivative Estimation: Analytic or Taylor?," Department of Economics Working Papers 2015-02, McMaster University.
    • Handle: RePEc:mcm:deptwp:2015-02
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    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2015-02.pdf
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    References listed on IDEAS

    as
    1. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    2. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
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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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    More about this item

    Keywords

    nonparametric; smoothing; constrained estimation;
    All these keywords.

    JEL classification:

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

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