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ESTIMATES OF DERIVATIVES OF (LOG) DENSITIES AND RELATED OBJECTS

Published online by Cambridge University Press:  27 December 2021

Joris Pinkse Open the ORCID record for Joris Pinkse [Opens in a new window]  and
Karl Schurter Open the ORCID record for Karl Schurter [Opens in a new window]
Joris Pinkse
Affiliation:
Pennsylvania State University
Karl Schurter*
Affiliation:
Pennsylvania State University
*
Address correspondence to Karl Schurter, Department of Economics, Pennsylvania State University, University Park, PA, USA; e-mail: kschurter@psu.edu.
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Abstract

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We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density function f. The estimator is guaranteed to be non-negative and achieves the same optimal rate of convergence in the interior as on the boundary of the support of f. The estimator is therefore well-suited to applications in which non-negative density estimates are required, such as in semiparametric maximum likelihood estimation. In addition, we show that our estimator compares favorably with other kernel-based methods, both in terms of asymptotic performance and computational ease. Simulation results confirm that our method can perform similarly or better in finite samples compared to these alternative methods when they are used with optimal inputs, that is, an Epanechnikov kernel and optimally chosen bandwidth sequence. We provide code in several languages.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 2 , April 2023 , pp. 321 - 356
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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