The Annals of Statistics

A constrained risk inequality with applications to nonparametric functional estimation

Lawrence D. Brown and Mark G. Low

Full-text: Open access

Abstract

A general constrained minimum risk inequality is derived. Given two densities $f_{\theta}$ and $f_0$ we find a lower bound for the risk at the point $\theta$ given an upper bound for the risk at the point 0. The inequality sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation.

Article information

Source
Ann. Statist., Volume 24, Number 6 (1996), 2524-2535.

Dates
First available in Project Euclid: 16 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032181166

Digital Object Identifier
doi:10.1214/aos/1032181166

Mathematical Reviews number (MathSciNet)
MR1425965

Zentralblatt MATH identifier
0867.62023

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures 62M99: None of the above, but in this section

Keywords
Adaptive estimation superefficient estimators nonparametric functional estimation minimum risk inequalities white noise model density estimation nonparametric regression

Citation

Brown, Lawrence D.; Low, Mark G. A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist. 24 (1996), no. 6, 2524--2535. doi:10.1214/aos/1032181166. https://projecteuclid.org/euclid.aos/1032181166


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