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dc.contributor.authorWied, Dominiken_US
dc.contributor.authorWeißbach, Rafaelen_US
dc.identifier.citationStatistical Papers 0932-5026 53 1 1-21 doi:10.1007/s00362-010-0338-1en_US
dc.description.abstractVarious 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.en_US
dc.description.otherRevised Version of: Technical Report No. 2009,03, Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund-
dc.publisherSpringer Berlin, Heidelberg-
dc.subject.keywordKernel estimationen_US
dc.subject.keywordPointwise consistencyen_US
dc.subject.keywordStrong uniform consistencyen_US
dc.subject.keywordEmpirical processen_US
dc.subject.keywordRate of convergenceen_US
dc.subject.keywordVariable bandwidthen_US
dc.titleConsistency of the kernel density estimator - a surveyen_US
Appears in Collections:Technical Reports, SFB 475: Komplexitätsreduktion in multivariaten Datenstrukturen, TU Dortmund
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