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

Book Contribution - Chapter

We consider pointwise consistency properties of kernel regression function type estimators where the bandwidth sequence in 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.
Book: Institute of Mathematical Statistics Collections
Series: High Dimensional Probability V: The Luminy volume
Volume: 5
Pages: 308-325
Number of pages: 18
ISBN:978-0-940600-78-2
Publication year:2009
Keywords:kernel regression function estimators