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September, 1992 Some Nonasymptotic Bounds for $L_1$ Density Estimation using Kernels
Somnath Datta
Ann. Statist. 20(3): 1658-1667 (September, 1992). DOI: 10.1214/aos/1176348791

Abstract

In this paper we obtain uniform upper bounds for the $L_1$ error of kernel estimators in estimating monotone densities and densities of bounded variation. The bounds are nonasymptotic and optimal in $n$, the sample size. For the bounded variation class, it is also optimal wrt an upper bound of the total variation. The proofs employ a one-sided kernel technique and are extremely simple.

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Somnath Datta. "Some Nonasymptotic Bounds for $L_1$ Density Estimation using Kernels." Ann. Statist. 20 (3) 1658 - 1667, September, 1992. https://doi.org/10.1214/aos/1176348791

Information

Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0782.62041
MathSciNet: MR1186272
Digital Object Identifier: 10.1214/aos/1176348791

Subjects:
Primary: 62G07
Secondary: 62C20

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 3 • September, 1992
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