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June 2004 Semiparametric density estimation by local L2-fitting
Kanta Naito
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Ann. Statist. 32(3): 1162-1191 (June 2004). DOI: 10.1214/009053604000000319


This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators proposed by several authors as special cases, and the asymptotic theories are developed. Theoretical comparison reveals that the estimators in this class are better than, or at least competitive with, the traditional kernel estimator in a broad class of densities. The asymptotically best estimator in this class can be obtained from the elegant feature of the bias function.


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Kanta Naito. "Semiparametric density estimation by local L2-fitting." Ann. Statist. 32 (3) 1162 - 1191, June 2004.


Published: June 2004
First available in Project Euclid: 24 May 2004

zbMATH: 1091.62023
MathSciNet: MR2065201
Digital Object Identifier: 10.1214/009053604000000319

Primary: 62G07
Secondary: 62G20

Keywords: Adjustment , Density estimation , ‎kernel‎ , local fitting , parametric model , semiparametic

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 3 • June 2004
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