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Integral functionals of the density

David M. Mason, Elizbar Nadaraya, and Grigol Sokhadze

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Abstract

We show how a simple argument based on an inequality of McDiarmid yields strong consistency and central limit results for plug-in estimators of integral functionals of the density.

Chapter information

Source
J. Antoch, M. Hušková and P.K. Sen, eds., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 153-168

Dates
First available in Project Euclid: 29 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1291044752

Digital Object Identifier
doi:10.1214/10-IMSCOLL716

Zentralblatt MATH identifier
1203.62056

Subjects
Primary: 62E05 62E20: Asymptotic distribution theory
Secondary: 62F07: Ranking and selection

Keywords
Integral functionals kernel density estimators inequalities consistency and central limit theorem

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Mason, David M.; Nadaraya, Elizbar; Sokhadze, Grigol. Integral functionals of the density. Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, 153--168, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL716. https://projecteuclid.org/euclid.imsc/1291044752


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References

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