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Browse Journals & Magazines > Information Theory, IEEE Tran ...> Volume:48 Issue:8 Help

Relative stability of global errors of nonparametric function estimators

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3 Author(s)
Gyorfi, L. ; Dept. of Comput. Sci. & Inf. Theor., Tech. Univ. Budapest, Hungary ; Schafer, D. ; Walk, H.

This paper presents relative stability properties of various nonparametric density estimators (histogram, kernel estimates) and of regression estimators (partitioning, kernel, and nearest neighbor estimates). In density estimation, let En denote the L1 error of an estimate calculated from n data, whereas in regression estimation, the L2 error of the estimate is used. Sufficient conditions for En/E{En}→1 in probability are provided. If this limit holds, the asymptotic behavior of the random error En can be characterized by its expectation E{En},, and one may apply, for example, the established rate-of-convergence results for E{En}.

Published in:
Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 8 )

Date of Publication: Aug 2002

Page(s):
2230 - 2242
ISSN :
0018-9448
INSPEC Accession Number:
7345253
Digital Object Identifier :
10.1109/TIT.2002.800491
Product Type:
Journals & Magazines
Date of Current Version :
07 August 2002
Issue Date :
Aug 2002
Sponsored by :
IEEE Information Theory Society

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