Consistency of the kernel density estimator - a survey
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Date
2009-04-30T10:40:09Z
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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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Keywords
Empirical process, Kernel estimation, Pointwise consistency, Rate of convergence, Strong uniform consistency, Variable bandwidth