## The Annals of Statistics

### On Bandwidth Variation in Kernel Estimates-A Square Root Law

Ian S. Abramson

#### 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