Consistency of the kernel density estimator a sur

Authors: Dominik Wied Rafael Weißbach

Publish Date: 2010/06/13

Volume: 53, Issue: 1, Pages: 1-21

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Abstract

Various consistency proofs for the kernel density estimator have been developed over the last few decades Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand While considering global properties of the empirical distribution functions is sufficient for strong consistency proofs of exact convergence rates use deeper information about the underlying empirical processes A unifying character however is that earlier and more recent proofs use bounds on the probability that a sum of random variables deviates from its mean

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