Translator Disclaimer
December, 1982 On Bandwidth Variation in Kernel Estimates-A Square Root Law
Ian S. Abramson
Ann. Statist. 10(4): 1217-1223 (December, 1982). DOI: 10.1214/aos/1176345986

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.

Citation

Download Citation

Ian S. Abramson. "On Bandwidth Variation in Kernel Estimates-A Square Root Law." Ann. Statist. 10 (4) 1217 - 1223, December, 1982. https://doi.org/10.1214/aos/1176345986

Information

Published: December, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0507.62040
MathSciNet: MR673656
Digital Object Identifier: 10.1214/aos/1176345986

Subjects:
Primary: 62G05
Secondary: 62F12

Rights: Copyright © 1982 Institute of Mathematical Statistics

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.10 • No. 4 • December, 1982
Back to Top