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VOL. 5 | 2009 Uniform in bandwidth consistency of kernel regression estimators at a fixed point
Julia Dony, Uwe Einmahl

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad


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.


Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.62052
MathSciNet: MR2797955

Digital Object Identifier: 10.1214/09-IMSCOLL520

Primary: 62G08

Keywords: consistency , Empirical processes , Exponential inequalities , Kernel estimation , Moment inequalities , Nadaraya–Watson , regression , uniform in bandwidth

Rights: Copyright © 2009, Institute of Mathematical Statistics


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