The Annals of Probability

A Second-Order Asymptotic Distributional Representation of $M$-Estimators with Discontinuous Score Functions

Jana Jureckova and Pranab Kumar Sen

Full-text: Open access

Abstract

For a nondecreasing score function having finitely many jump discontinuities, a representation of $M$-estimators with the second-order asymptotic distribution is established, and the result is also extended to one-step versions of $M$-estimators.

Article information

Source
Ann. Probab., Volume 15, Number 2 (1987), 814-823.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992174

Digital Object Identifier
doi:10.1214/aop/1176992174

Mathematical Reviews number (MathSciNet)
MR885146

Zentralblatt MATH identifier
0635.62017

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62E20: Asymptotic distribution theory 62F35: Robustness and adaptive procedures 62G05: Estimation

Keywords
Jump discontinuity $M$-estimator one-step version of $M$-estimator random change of time weak convergence of $M$-processes

Citation

Jureckova, Jana; Sen, Pranab Kumar. A Second-Order Asymptotic Distributional Representation of $M$-Estimators with Discontinuous Score Functions. Ann. Probab. 15 (1987), no. 2, 814--823. doi:10.1214/aop/1176992174. https://projecteuclid.org/euclid.aop/1176992174


Export citation