The Annals of Statistics

Asymptotics for $M$-Estimators Defined by Convex Minimization

Wojciech Niemiro

Full-text: Open access

Abstract

We consider $M$-estimators defined by minimization of a convex criterion function, not necessarily smooth. Our asymptotic results generalize some of those concerning the LAD estimators. We establish a Bahadur-type strong approximation and bounds on the rate of convergence.

Article information

Source
Ann. Statist., Volume 20, Number 3 (1992), 1514-1533.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348782

Digital Object Identifier
doi:10.1214/aos/1176348782

Mathematical Reviews number (MathSciNet)
MR1186263

Zentralblatt MATH identifier
0786.62040

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62F20

Keywords
$M$-estimation convex minimization asymptotics least absolute deviations Bahadur representation

Citation

Niemiro, Wojciech. Asymptotics for $M$-Estimators Defined by Convex Minimization. Ann. Statist. 20 (1992), no. 3, 1514--1533. doi:10.1214/aos/1176348782. https://projecteuclid.org/euclid.aos/1176348782


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