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Local Polynomial Derivative Estimation: Analytic or Taylor?

Essays in Honor of Aman Ullah

ISBN: 978-1-78560-787-5, eISBN: 978-1-78560-786-8

Publication date: 23 June 2016

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.

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Acknowledgements

Acknowledgements

I would like to express my deepest gratitude to Aman Ullah for his encouragement and guidance over the course of my education and career. I would also like to acknowledge Chris Parmeter for his encouragement and feedback, and with whom previous work and discussions provided the groundwork for this paper, and to thank Carlos Ordas Criado for the illustrative example used herein. Finally, I would like to gratefully acknowledge support from the Natural Sciences and Engineering Research Council of Canada (NSERC:www.nserc.ca), the Social Sciences and Humanities Research Council of Canada (SSHRC:www.sshrc.ca), and the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca).

Citation

Racine, J.S. (2016), "Local Polynomial Derivative Estimation: Analytic or Taylor?", Essays in Honor of Aman Ullah (Advances in Econometrics, Vol. 36), Emerald Group Publishing Limited, Leeds, pp. 617-633. https://doi.org/10.1108/S0731-905320160000036027

Publisher

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Emerald Group Publishing Limited

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