Consistency of the kernel density estimator - a survey - Dominik Wied; Rafael Weißbach (Statistical Papers, 2010)
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.
urn:nbn:de:101:1-201607293734; hdl:2003/26095; Additional information: Accepted Manuscript Version of: Technical Report No. 2009,03, Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund
Keywords: 519; Kernel estimation; Pointwise consistency; Strong uniform consistency; Empirical process; Rate of convergence; Variable bandwidth