The Annals of Statistics

A New Class of Kernels for Nonparametric Curve Estimation

Karen Messer and Larry Goldstein

Full-text: Open access

Abstract

We introduce a new class of variable kernels which depend on the smoothing parameter b through a simple scaling operation, and which have good integrated mean square error (IMSE) convergence properties. These kernels deform "automatically" near the boundary, eliminating boundary bias. Computational formulas are given for all orders of kernel in terms of exponentially damped sines and cosines. The kernel is a computationally convenient approximation to a certain Green's function, with the resulting kernel estimate closely related to a smoothing spline estimate.

Article information

Source
Ann. Statist., Volume 21, Number 1 (1993), 179-195.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349021

Digital Object Identifier
doi:10.1214/aos/1176349021

Mathematical Reviews number (MathSciNet)
MR1212172

Zentralblatt MATH identifier
0777.62041

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62J02: General nonlinear regression

Keywords
Nonparametric curve estimation kernel boundary bias Green's function

Citation

Messer, Karen; Goldstein, Larry. A New Class of Kernels for Nonparametric Curve Estimation. Ann. Statist. 21 (1993), no. 1, 179--195. doi:10.1214/aos/1176349021. https://projecteuclid.org/euclid.aos/1176349021


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