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June, 1983 On the Asymptotic Relation Between $L$-Estimators and $M$-Estimators and their Asymptotic Efficiency Relative to the Cramer-Rao Lower Bound
Constance van Eeden
Ann. Statist. 11(2): 674-690 (June, 1983). DOI: 10.1214/aos/1176346172

Abstract

This paper gives conditions under which $L$- and $M$-estimators of a location parameter have asymptotically the same distribution, conditions under which they are asymptotically equivalent and conditions under which $L$-estimators are asymptotically efficient relative to the Cramer-Rao lower bound. Our results differ from analogous results of Jung (1955), Bickel (1965), Chernoff, Gastwirth, Johns (1967), Jaeckel (1971) and Rivest (1978, 1982) in that we do not require that the derivative of the density of the observations is absolutely continuous nor that the function defining the $M$-estimator is absolutely continuous.

Citation

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Constance van Eeden. "On the Asymptotic Relation Between $L$-Estimators and $M$-Estimators and their Asymptotic Efficiency Relative to the Cramer-Rao Lower Bound." Ann. Statist. 11 (2) 674 - 690, June, 1983. https://doi.org/10.1214/aos/1176346172

Information

Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0526.62038
MathSciNet: MR696078
Digital Object Identifier: 10.1214/aos/1176346172

Subjects:
Primary: 62G05
Secondary: 62F10

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 2 • June, 1983
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