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September, 1994 Estimators Related to $U$-Processes with Applications to Multivariate Medians: Asymptotic Normality
Miguel A. Arcones, Zhiqiang Chen, Evarist Gine
Ann. Statist. 22(3): 1460-1477 (September, 1994). DOI: 10.1214/aos/1176325637

Abstract

If a criterion function $g(x_1, \ldots, x_m; \theta)$ depends on $m > 1$ samples, then a natural estimator of $\arg \max P^mg(x_1, \ldots, x_m; \theta)$ is the $\arg \max$ of a $U$-process. It is observed that, under suitable conditions, these estimators are asymptotically normal. This is then applied to prove asymptotic normality of Liu's simplical median and of Oja's medians in $\mathbb{R}^d$.

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Miguel A. Arcones. Zhiqiang Chen. Evarist Gine. "Estimators Related to $U$-Processes with Applications to Multivariate Medians: Asymptotic Normality." Ann. Statist. 22 (3) 1460 - 1477, September, 1994. https://doi.org/10.1214/aos/1176325637

Information

Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0827.62023
MathSciNet: MR1311984
Digital Object Identifier: 10.1214/aos/1176325637

Subjects:
Primary: 62F12
Secondary: 62E20

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 3 • September, 1994
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