Translator Disclaimer
June 2000 On the asymptotics of constrained local $M$-estimators
Alexander Shapiro
Ann. Statist. 28(3): 948-960 (June 2000). DOI: 10.1214/aos/1015952006

Abstract

We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and,more generally, $M$-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set $S$.We give a counterexample showing that regularity of $S$ in the sense of Clarke is not sufficient for asymptotic equivalence of $\sqrt{n}$-consistent locally optimal $M$-estimators.We argue further that stronger properties, such as so-called near convexity or prox-regularity of $S$ are required in order to ensure that any two $\sqrt{n}$-consistent locally optimal $M$-estimators have the same asymptotics.

Citation

Download Citation

Alexander Shapiro. "On the asymptotics of constrained local $M$-estimators." Ann. Statist. 28 (3) 948 - 960, June 2000. https://doi.org/10.1214/aos/1015952006

Information

Published: June 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62305
MathSciNet: MR1792795
Digital Object Identifier: 10.1214/aos/1015952006

Subjects:
Primary: 62F12

Rights: Copyright © 2000 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.28 • No. 3 • June 2000
Back to Top