The Annals of Statistics

Some Nonasymptotic Bounds for $L_1$ Density Estimation using Kernels

Somnath Datta

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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.

Article information

Source
Ann. Statist., Volume 20, Number 3 (1992), 1658-1667.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348791

Digital Object Identifier
doi:10.1214/aos/1176348791

Mathematical Reviews number (MathSciNet)
MR1186272

Zentralblatt MATH identifier
0782.62041

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62C20: Minimax procedures

Keywords
Monotone density density of bounded variation $L_1$ estimation minimax risk kernel estimator nonasymptotic bound

Citation

Datta, Somnath. Some Nonasymptotic Bounds for $L_1$ Density Estimation using Kernels. Ann. Statist. 20 (1992), no. 3, 1658--1667. doi:10.1214/aos/1176348791. https://projecteuclid.org/euclid.aos/1176348791


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