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August 2003 On M-estimators and normal quantiles
Andrzej S. Kozek
Ann. Statist. 31(4): 1170-1185 (August 2003). DOI: 10.1214/aos/1059655910

Abstract

This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators offer considerable reduction of variance at near normal probability distributions.

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Andrzej S. Kozek. "On M-estimators and normal quantiles." Ann. Statist. 31 (4) 1170 - 1185, August 2003. https://doi.org/10.1214/aos/1059655910

Information

Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1041.62018
MathSciNet: MR2001647
Digital Object Identifier: 10.1214/aos/1059655910

Subjects:
Primary: 62F35
Secondary: 62F12

Keywords: $a$-quantiles , $M$-estimator , $M$-functional , asymptotics , normal quantiles , robust

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • August 2003
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