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UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION AND ITS DERIVATIVES WHEN THE DENSITY HAS A KNOWN POLE

Published online by Cambridge University Press:  13 June 2025

Sorawoot SrisumaOpen the ORCID record for Sorawoot Srisuma[Opens in a new window]
Sorawoot Srisuma*
Affiliation:
National University of Singapore
*
Address correspondence to Department of Economics, National University of Singapore, Singapore, e-mail: s.srisuma@nus.edu.sg.
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Abstract

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We study the uniform convergence rates of nonparametric estimators for a probability density function and its derivatives when the density has a known pole. Such situations arise in some structural microeconometric models, for example, in auction, labor, and consumer search, where uniform convergence rates of density functions are important for nonparametric and semiparametric estimation. Existing uniform convergence rates based on Rosenblatt’s kernel estimator are derived under the assumption that the density is bounded. They are not applicable when there is a pole in the density. We treat the pole nonparametrically and show various kernel-based estimators can attain any convergence rate that is slower than the optimal rate when the density is bounded uniformly over an appropriately expanding support under mild conditions.

Information

Type
ARTICLE
Information
Econometric Theory , Volume 42 , Issue 3 , June 2026, pp. 631 - 657
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), 2025. Published by Cambridge University Press

Footnotes

I thank Oliver Linton and two anonymous referees for their insightful comments and suggestions that helped substantially improve the article.

References

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