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August, 1972 A Note on Huber's Robust Estimation of a Location Parameter
Jerome Sacks, Donald Ylvisaker
Ann. Math. Statist. 43(4): 1068-1075 (August, 1972). DOI: 10.1214/aoms/1177692460


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 $\varepsilon > \varepsilon_0$.


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Jerome Sacks. Donald Ylvisaker. "A Note on Huber's Robust Estimation of a Location Parameter." Ann. Math. Statist. 43 (4) 1068 - 1075, August, 1972.


Published: August, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0284.62022
MathSciNet: MR317476
Digital Object Identifier: 10.1214/aoms/1177692460

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 4 • August, 1972
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