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January, 1977 Bounds for Estimation of Density Functions and Their Derivatives
Terry G. Meyer
Ann. Statist. 5(1): 136-142 (January, 1977). DOI: 10.1214/aos/1176343746


Lower bounds on the radius of various confidence sets for density functions and their derivatives are determined. In each case investigated, the smallest radius obtainable and the radius actually obtained by using known estimates exhibit the same dependency on the fixed sample size $n$. The lower bounds are derived using methods in Meyer (1976). Although only a few combinations of pseudometric and density class are considered here, the techniques illustrated can be used elsewhere with little conceptual difficulty.


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Terry G. Meyer. "Bounds for Estimation of Density Functions and Their Derivatives." Ann. Statist. 5 (1) 136 - 142, January, 1977.


Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0357.62024
MathSciNet: MR464484
Digital Object Identifier: 10.1214/aos/1176343746

Primary: 62G05
Secondary: 62G15

Keywords: Density estimation , minimal radius confidence set , probability convergence of density estimates

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • January, 1977
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