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June, 1982 $L$- and $R$-Estimation and the Minimax Property
Jerome Sacks, Donald Ylvisaker
Ann. Statist. 10(2): 643-645 (June, 1982). DOI: 10.1214/aos/1176345808


Let $\{X_i\}$ be a sample from $F(x - \theta)$ where $F$ is in a class $\mathscr{F}$ of symmetric distributions on the line and $\theta$ is the location parameter to be estimated. Huber has shown that maximum likelihood estimation has a minimax property over a convex $\mathscr{F}$. Here a simple convex $\mathscr{F}$ is given for which neither $L$- nor $R$-estimation has the minimax property. In particular, this example shows that a recent assertion concerning $L$-estimation is not true.


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Jerome Sacks. Donald Ylvisaker. "$L$- and $R$-Estimation and the Minimax Property." Ann. Statist. 10 (2) 643 - 645, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0488.62022
MathSciNet: MR653542
Digital Object Identifier: 10.1214/aos/1176345808

Primary: 62G35
Secondary: 62G20

Keywords: Location parameter estimation , minimax property , robust estimation

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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