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Uniform in bandwidth consistency of kernel regression estimators at a fixed point

Julia Dony and Uwe Einmahl

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Abstract

We consider pointwise consistency properties of kernel regression function type estimators where the bandwidth sequence is not necessarily deterministic. In some recent papers uniform convergence rates over compact sets have been derived for such estimators via empirical process theory. We now show that it is possible to get optimal results in the pointwise case as well. The main new tool for the present work is a general moment bound for empirical processes which may be of independent interest.

Chapter information

Source
Christian Houdré, Vladimir Koltchinskii, David M. Mason and Magda Peligrad, eds., High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 308-325

Dates
First available in Project Euclid: 2 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1265119276

Digital Object Identifier
doi:10.1214/09-IMSCOLL520

Mathematical Reviews number (MathSciNet)
MR2797955

Zentralblatt MATH identifier
1243.62052

Subjects
Primary: 62G08: Nonparametric regression

Keywords
kernel estimation Nadaraya–Watson regression uniform in bandwidth consistency empirical processes exponential inequalities moment inequalities

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

Dony, Julia; Einmahl, Uwe. Uniform in bandwidth consistency of kernel regression estimators at a fixed point. High Dimensional Probability V: The Luminy Volume, 308--325, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-IMSCOLL520. https://projecteuclid.org/euclid.imsc/1265119276


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References

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