Open Access
Translator Disclaimer
December, 1983 On the Minimax Property for $R$-Estimators of Location
John R. Collins
Ann. Statist. 11(4): 1190-1195 (December, 1983). DOI: 10.1214/aos/1176346331

Abstract

Consider the problem of estimating the unknown location parameter $\theta$ based on a random sample from $F(x - \theta)$, where $F$ is an unknown member of the class of distribution functions $\mathscr{F} = \{F: F$ is symmetric about 0 and $\sup_x |F(x) - \Phi(x)| \leq \varepsilon\}$, where $\Phi$ denotes the standard normal distribution function. Huber (1964) showed that $M$-estimation has a minimax property for this model, whereas Sacks and Ylvisaker (1972) showed that $L$-estimation fails to have the minimax property. It is shown here that $R$-estimation does have the minimax property for this model.

Citation

Download Citation

John R. Collins. "On the Minimax Property for $R$-Estimators of Location." Ann. Statist. 11 (4) 1190 - 1195, December, 1983. https://doi.org/10.1214/aos/1176346331

Information

Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0542.62024
MathSciNet: MR720263
Digital Object Identifier: 10.1214/aos/1176346331

Subjects:
Primary: 62G35
Secondary: 62G05

Keywords: $R$-estimators , minimax property , Robust estimation of location

Rights: Copyright © 1983 Institute of Mathematical Statistics

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.11 • No. 4 • December, 1983
Back to Top