Uniform in bandwidth consistency of kernel regression estimators at a fixed point
Julia Dony, Uwe Einmahl
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.
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Primary Subjects: 62G08
Keywords: kernel estimation; Nadaraya–Watson; regression; uniform in bandwidth; consistency; empirical processes; exponential inequalities; moment inequalities
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1265119276
Digital Object Identifier: doi:10.1214/09-IMSCOLL520
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