The Annals of Mathematical Statistics

Existence and Consistency of Modified Minimum Contrast Estimates

D. Landers

Full-text: Open access

Abstract

It is the purpose of this paper to explore the efficiency of a modified definition for maximum likelihood estimates which depends on the whole equivalence class of densities only and not--as in the classical case--on the particular choice of versions. We prove the existence of measurable maximum likelihood estimates in the new sense for compact metrizable families of probability measures without any continuity assumption for the densities. For appropriate families of probability measures the modified asymptotic maximum likelihood estimates are exactly the strongly consistent estimates. The paper uses Huber's concept of minimum contrast estimates which covers maximum likelihood estimates as a special case.

Article information

Source
Ann. Math. Statist., Volume 43, Number 1 (1972), 74-83.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692702

Digital Object Identifier
doi:10.1214/aoms/1177692702

Mathematical Reviews number (MathSciNet)
MR311023

Zentralblatt MATH identifier
0238.62031

JSTOR
links.jstor.org

Citation

Landers, D. Existence and Consistency of Modified Minimum Contrast Estimates. Ann. Math. Statist. 43 (1972), no. 1, 74--83. doi:10.1214/aoms/1177692702. https://projecteuclid.org/euclid.aoms/1177692702


Export citation