The Annals of Mathematical Statistics

A Note on Huber's Robust Estimation of a Location Parameter

Jerome Sacks and Donald Ylvisaker

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Abstract

Huber, in his fundamental paper [1] and in [2], has considered the robust estimation of a location parameter and has obtained results which he applied to some examples including the $\varepsilon$-normal model, $\{F|\sup_x|F(x) - \Phi(x)\mid \leqq \varepsilon, F \text{symmetric}\}$, when $\varepsilon$ is sufficiently small $(\varepsilon \leqq \varepsilon_0 \sim .03)$. In this note we show how his methods work for the family of distributions $\{F \mid \int^A_{-A} dF \geqq p, F \text{symmetric}\}$ and then use this to solve the $\varepsilon$-normal problem when $\varepsilon > \varepsilon_0$.

Article information

Source
Ann. Math. Statist., Volume 43, Number 4 (1972), 1068-1075.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692460

Digital Object Identifier
doi:10.1214/aoms/1177692460

Mathematical Reviews number (MathSciNet)
MR317476

Zentralblatt MATH identifier
0284.62022

JSTOR
links.jstor.org

Citation

Sacks, Jerome; Ylvisaker, Donald. A Note on Huber's Robust Estimation of a Location Parameter. Ann. Math. Statist. 43 (1972), no. 4, 1068--1075. doi:10.1214/aoms/1177692460. https://projecteuclid.org/euclid.aoms/1177692460


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