Open Access
September, 1980 On Improving Convergence Rates for Nonnegative Kernel Density Estimators
George R. Terrell, David W. Scott
Ann. Statist. 8(5): 1160-1163 (September, 1980). DOI: 10.1214/aos/1176345153

Abstract

To improve the rate of decrease of integrated mean square error for nonparametric kernel density estimators beyond $0(n^{-\frac{4}{5}}),$ we must relax the constraint that the density estimate be a bonafide density function, that is, be nonnegative and integrate to one. All current methods for kernel (and orthogonal series) estimators relax the nonnegativity constraint. In this paper we show how to achieve similar improvement by relaxing the integral constraint only. This is important in applications involving hazard function and likelihood ratios where negative density estimates are awkward to handle.

Citation

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George R. Terrell. David W. Scott. "On Improving Convergence Rates for Nonnegative Kernel Density Estimators." Ann. Statist. 8 (5) 1160 - 1163, September, 1980. https://doi.org/10.1214/aos/1176345153

Information

Published: September, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0459.62031
MathSciNet: MR585714
Digital Object Identifier: 10.1214/aos/1176345153

Subjects:
Primary: 62G05

Keywords: Kernel estimation , Nonparametric density estimation , rates of convergence

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • September, 1980
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