Relative stability of global errors of nonparametric function estimators

Author

Györfi, László ; Schäfer, Dominik ; Walk, Harro

Author_Institution

Dept. of Comput. Sci. & Inf. Theor., Tech. Univ. Budapest, Hungary

Volume

48

Issue

8

fYear

2002

fDate

8/1/2002 12:00:00 AM

Firstpage

2230

Lastpage

2242

Abstract

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 E_n/E{E_n}→1 in probability are provided. If this limit holds, the asymptotic behavior of the random error E_n can be characterized by its expectation E{E_n},, and one may apply, for example, the established rate-of-convergence results for E{En}.

Keywords

error analysis; nonparametric statistics; numerical stability; recursive estimation; bandwidth; convergence rate; global errors; histogram; identically distributed random variables; kernel estimates; nearest neighbor estimates; nonparametric density estimators; nonparametric function estimators; partitioning; probability; regression estimators; relative stability properties; sufficient conditions; upper bound; Computer errors; Convergence; Estimation error; H infinity control; Histograms; Kernel; Nearest neighbor searches; Random variables; Stability; Sufficient conditions;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.800491

Filename

1019835