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July, 1978 Lower Bounds for Nonparametric Density Estimation Rates
David W. Boyd, J. Michael Steele
Ann. Statist. 6(4): 932-934 (July, 1978). DOI: 10.1214/aos/1176344269

Abstract

If $f_n(x)$ is any estimator of the density $f(x),$ it is proved that the mean integrated square error is no better than $O(n^{-1}).$

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David W. Boyd. J. Michael Steele. "Lower Bounds for Nonparametric Density Estimation Rates." Ann. Statist. 6 (4) 932 - 934, July, 1978. https://doi.org/10.1214/aos/1176344269

Information

Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62044
MathSciNet: MR494674
Digital Object Identifier: 10.1214/aos/1176344269

Subjects:
Primary: 62G20
Secondary: 62F20

Keywords: Cramer-Rao inequality , Density estimation , mean integrated square error , nonparametric

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • July, 1978
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