Open Access
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


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.


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Ian S. Abramson. "On Bandwidth Variation in Kernel Estimates-A Square Root Law." Ann. Statist. 10 (4) 1217 - 1223, December, 1982.


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

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

Primary: 62G05
Secondary: 62F12

Keywords: bandwidth variation , bias reduction , Equivariance , inverse square root , kernel estimate , logogram

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 4 • December, 1982
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