publication . Other literature type . Article . 1995

Improved Variable Window Kernel Estimates of Probability Densities

Tien-Chung Hu; Peter Hall; James Stephen Marron;
Open Access English
  • Published: 01 Feb 1995
  • Publisher: The Institute of Mathematical Statistics
Abstract
Variable window width kernel density estimators, with the width varying proportionally to the square root of the density, have been thought to have superior asymptotic properties. The rate of convergence has been claimed to be as good as those typical for higher-order kernels, which makes the variable width estimators more attractive because no adjustment is needed to handle the negativity usually entailed by the latter. However, in a recent paper, Terrell and Scott show that these results can fail in important cases. In this paper, we characterize situations where the fast rate is valid, and also give rates for a variety of cases where they are slower. In addit...
Subjects
free text keywords: Adaptive methods, bandwidth choice, curve estimation, nonparametric estimation, smoothing, 62G05, Statistics, Probability and Uncertainty, Statistics and Probability, Convergence (routing), Estimator, Rate of convergence, Kernel density estimation, Mathematics, Kernel method, Probability density function, Square root, Applied mathematics, Statistics
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