Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/39692
Authors: 
Wied, Dominik
Weißbach, Rafael
Year of Publication: 
2010
Citation: 
[Journal:] Statistical Papers [ISSN:] 0932-5026 [Volume:] 53 [Issue:] 1 [Pages:] 1-21 [DOI/URN:] doi:10.1007/s00362-010-0338-1
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.
Subjects: 
Kernel estimation
Pointwise consistency
Strong uniform consistency
Empirical process
Rate of convergence
Variable bandwidth
Persistent Identifier of the first edition: 
Additional Information: 
Revised Version of: Technical Report No. 2009,03, Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund
Document Type: 
Article

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