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October 1999 Optimal convergence rates for Good's nonparametric maximum likelihood density estimator
P. P. B. Eggermont, V. N. LaRiccia
Ann. Statist. 27(5): 1600-1615 (October 1999). DOI: 10.1214/aos/1017939143

Abstract

We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to $L^1$ convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the roughness penalized estimator.

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P. P. B. Eggermont. V. N. LaRiccia. "Optimal convergence rates for Good's nonparametric maximum likelihood density estimator." Ann. Statist. 27 (5) 1600 - 1615, October 1999. https://doi.org/10.1214/aos/1017939143

Information

Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0957.62039
MathSciNet: MR2001A:62045
Digital Object Identifier: 10.1214/aos/1017939143

Subjects:
Primary: 62G07

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 5 • October 1999
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