The Annals of Statistics

On Bandwidth Variation in Kernel Estimates-A Square Root Law

Ian S. Abramson

Full-text: Open access

Abstract

We consider kernel estimation of a smooth density $f$ at a point, but depart from the usual approach in admitting an adaptive dependence of the sharpness of the kernels on the underlying density. Proportionally varying the bandwidths like $f^{-1/2}$ at the contributing readings lowers the bias to a vanishing fraction of the usual value, and makes for performance seen in well-known estimators that force moment conditions on the kernel (and so sacrifice positivity of the curve estimate). Issues of equivariance and variance stabilitization are treated.

Article information

Source
Ann. Statist. Volume 10, Number 4 (1982), 1217-1223.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345986

Digital Object Identifier
doi:10.1214/aos/1176345986

Mathematical Reviews number (MathSciNet)
MR673656

Zentralblatt MATH identifier
0507.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Kernel estimate bandwidth variation inverse square root bias reduction equivariance logogram

Citation

Abramson, Ian S. On Bandwidth Variation in Kernel Estimates-A Square Root Law. Ann. Statist. 10 (1982), no. 4, 1217--1223. doi:10.1214/aos/1176345986. https://projecteuclid.org/euclid.aos/1176345986.


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