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December, 1986 On Improving Density Estimators which are not Bona Fide Functions
Leslaw Gajek
Ann. Statist. 14(4): 1612-1618 (December, 1986). DOI: 10.1214/aos/1176350182

Abstract

In order to improve the rate of decrease of the IMSE for nonparametric kernel density estimators with nonrandom bandwidth beyond $O(n^{-4/5})$ all current methods must relax the constraint that the density estimate be a bona fide function, that is, be nonnegative and integrate to one. In this paper we show how to achieve similar improvement without relaxing any of these constraints. The method can also be applied for orthogonal series, adaptive orthogonal series, spline, jackknife, and other density estimators, and assures an improvement of the IMSE for each sample size.

Citation

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Leslaw Gajek. "On Improving Density Estimators which are not Bona Fide Functions." Ann. Statist. 14 (4) 1612 - 1618, December, 1986. https://doi.org/10.1214/aos/1176350182

Information

Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0623.62034
MathSciNet: MR868324
Digital Object Identifier: 10.1214/aos/1176350182

Subjects:
Primary: 62G05

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • December, 1986
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