The Annals of Statistics

A Note on the Consistency of Maximum Likelihood Estimates for Finite Families of Stochastic Processes

P. E. Caines

Full-text: Open access

Abstract

We consider families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes it is shown that maximum likelihood estimates convergence almost surely to the correct parameter value. This established by use of a submartingale property of the sequence of maximized likelihood ratios together with a technique first employed by Wald [24] in the case of independently identically distributed random variables.

Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 539-546.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343086

Digital Object Identifier
doi:10.1214/aos/1176343086

Mathematical Reviews number (MathSciNet)
MR368255

Zentralblatt MATH identifier
0303.62022

JSTOR
links.jstor.org

Keywords
6215 Asymptotic Theory 6220 Estimation Parametric Case Parameter estimation maximum likelihood estimation

Citation

Caines, P. E. A Note on the Consistency of Maximum Likelihood Estimates for Finite Families of Stochastic Processes. Ann. Statist. 3 (1975), no. 2, 539--546. doi:10.1214/aos/1176343086. https://projecteuclid.org/euclid.aos/1176343086


Export citation