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Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen >
Technical Reports, SFB 475, TU Dortmund >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10419/39692
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| Title: | | Consistency of the kernel density estimator - a survey  |
| Authors: | | Wied, Dominik Weißbach, Rafael |
| Issue Date: | | 2010 |
| Citation: | | [Journal:] Statistical Papers [ISSN:] 0932-5026 [Pages:] 1-21 [Publisher:] Springer [Place:] Berlin / Heidelberg [URL:] http://dx.doi.org/10.1007/s00362-010-0338-1 [DOI/URN:] 10.1007/s00362-010-0338-1 |
| Series/Report no.: | | Technical Report // Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2009,03 [rev.] |
| 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 |
| Appears in Collections: | | Articles / Aufsätze Technical Reports, SFB 475, TU Dortmund
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| tr03-09.pdf | | 208.42 kB | Adobe PDF |
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