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February 2001 Optimal Robust M-Estimates of Location
Ricardo Fraiman, Víctor J. Yohai, Ruben H. Zamar
Ann. Statist. 29(1): 194-223 (February 2001). DOI: 10.1214/aos/996986506


We find optimal robust estimates for the location parameter of n independent measurements from a common distribution F that belongs to a contamination neighborhood of a normal distribution. We follow an asymptotic minimax approach similar to Huber's but work with full neighborhoods of the central parametric model including nonsymmetric distributions. Our optimal estimates minimize monotone functions of the estimate's asymptotic variance and bias, which include asymptotic approximations for the quantiles of the estimate's distribution. In particular, we obtain robust asymptotic confidence intervals of minimax length.


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Ricardo Fraiman. Víctor J. Yohai. Ruben H. Zamar. "Optimal Robust M-Estimates of Location." Ann. Statist. 29 (1) 194 - 223, February 2001.


Published: February 2001
First available in Project Euclid: 5 August 2001

zbMATH: 1029.62019
MathSciNet: MR1833963
Digital Object Identifier: 10.1214/aos/996986506

Primary: 62F35

Keywords: M-estimates , minimax intervals , robust location

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 1 • February 2001
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