## The Annals of Statistics

### Some Nonasymptotic Bounds for $L_1$ Density Estimation using Kernels

Somnath Datta

#### 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
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