Annals of Statistics

On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice

Francis Comets

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Abstract

We prove strong consistency of a class of maximum objective estimators for exponential parametric families of Markov random fields on $\mathbb{Z}^d$, including both maximum likelihood and pseudolikelihood estimators, using large deviation estimates. We also obtain the optimality property for the maximum likelihood estimator in the sense of Bahadur.

Article information

Source
Ann. Statist., Volume 20, Number 1 (1992), 455-468.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348532

Digital Object Identifier
doi:10.1214/aos/1176348532

Mathematical Reviews number (MathSciNet)
MR1150354

Zentralblatt MATH identifier
0787.62100

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62M05: Markov processes: estimation 82A25 60G60: Random fields

Keywords
Maximum likelihood estimator pseudolikelihood Markov random field objective function Bahadur efficiency large deviation

Citation

Comets, Francis. On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice. Ann. Statist. 20 (1992), no. 1, 455--468. doi:10.1214/aos/1176348532. https://projecteuclid.org/euclid.aos/1176348532


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