Open Access
February 2021 Nonparametric estimation of surface integrals on level sets
Wanli Qiao
Bernoulli 27(1): 155-191 (February 2021). DOI: 10.3150/20-BEJ1232


Surface integrals on density level sets often appear in asymptotic results of nonparametric level set estimation, such as for confidence regions and bandwidth selection. Also surface integrals can be used to describe the shape of level sets. Assuming the integrands are known, we consider three estimators of the surface integrals on density level sets, one as a direct plug-in estimator, and the other two based on different neighborhoods of level sets. For all the three estimators, we derive the rates of convergence and asymptotic distributions.


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Wanli Qiao. "Nonparametric estimation of surface integrals on level sets." Bernoulli 27 (1) 155 - 191, February 2021.


Received: 1 November 2019; Revised: 1 April 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282846
MathSciNet: MR4177365
Digital Object Identifier: 10.3150/20-BEJ1232

Keywords: curvatures , kernel density estimation , Level sets , positive reach , surface integrals

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

Vol.27 • No. 1 • February 2021
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