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Uniform in bandwidth limit laws for kernel distribution function estimators

David M. Mason and Jan W. H. Swanepoel

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Abstract

We use results from modern empirical process theory to establish a uniform in bandwidth central limit theorem, laws of the iterated logarithm and Glivenko–Cantelli theorem for kernel distribution function estimators.

Chapter information

Source
Banerjee, M., Bunea, F., Huang, J., Koltchinskii, V., and Maathuis, M. H., eds., From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 241-253

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1362751191

Digital Object Identifier
doi:10.1214/12-IMSCOLL917

Zentralblatt MATH identifier
1327.62154

Keywords
62F15 62G07 62G08 Empirical processes kernel estimation distribution function and uniform in bandwidth

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Mason, David M.; Swanepoel, Jan W. H. Uniform in bandwidth limit laws for kernel distribution function estimators. From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, 241--253, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL917. https://projecteuclid.org/euclid.imsc/1362751191


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References

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