The Annals of Statistics

Bahadur representation of $M\sb m$ estimates

Arup Bose

Full-text: Open access

Abstract

We take a unified approach to asymptotic properties of $M_m$ estimates based on i.i.d. observations defined through the minimization of a real-valued criterion function of one or more variables. Our results are applicable to a host of location and scale estimators found in the literature.

Article information

Source
Ann. Statist., Volume 26, Number 2 (1998), 771-777.

Dates
First available in Project Euclid: 31 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028144859

Digital Object Identifier
doi:10.1214/aos/1028144859

Mathematical Reviews number (MathSciNet)
MR1626020

Zentralblatt MATH identifier
0929.62019

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations 60F15: Strong theorems 62E20: Asymptotic distribution theory 62F10: Point estimation 62G30: Order statistics; empirical distribution functions 62G35: Robustness 62H10: Distribution of statistics 62H12: Estimation 62J05: Linear regression

Keywords
$M$ estimates $U$ statistics asymptotic normality Bahadur representation measures of location measures of dispersion $L^1$ median Oja median $L^t$ estimates Hodges-Lehmann estimate generalized order statistics

Citation

Bose, Arup. Bahadur representation of $M\sb m$ estimates. Ann. Statist. 26 (1998), no. 2, 771--777. doi:10.1214/aos/1028144859. https://projecteuclid.org/euclid.aos/1028144859


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