On consistency of a class of estimators for exponential families of Markov random fields on the lattice
type: Item
instance of: scholarly article
title: On consistency of a class of estimators for exponential families of Markov random fields on the lattice
zbMATH Open document ID: 0787.62100
author: Francis Comets
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: A statistical estimation problem is considered for parametric exponential non-Gaussian families of Markov random fields, and more generally, Gibbs distributions (GD). Consistency, exponential convergence rates and Bahadur optimality are proved for the maximum and pseudo-maximum likelihood estimators under conditions allowing nonergodic, nonstationary and phase transition cases. The proofs are based on the large deviations estimates for the GD obtained by \textit{the author} [C. R. Acad. Sci., Paris, Ser. I 303, 511- 513 (1986; Zbl 0606.60035)], \textit{H. Föllmer} and \textit{S. Orey} [Ann. Probab. 16, No. 3, 961-977 (1988; Zbl 0648.60028)] and by \textit{S. Olla} [Probab. Theory Relat. Fields 77, No. 3, 343-357 (1988; Zbl 0621.60031)].
Mathematics Subject Classification ID: 62M40
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 61849
zbMATH Keywords: maximum likelihood
zbMATH Keywords: consistency
zbMATH Keywords: parametric exponential non-Gaussian families of Markov random fields
zbMATH Keywords: Gibbs distributions
zbMATH Keywords: convergence rates
zbMATH Keywords: Bahadur optimality
zbMATH Keywords: pseudo-maximum likelihood estimators
zbMATH Keywords: nonergodic
zbMATH Keywords: nonstationary
zbMATH Keywords: phase transition
zbMATH Keywords: large deviations estimates
reviewed by: Evgeni Trofimov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348532
OpenAlex ID: W1980164324
DOI: 10.1214/AOS/1176348532
description: scientific article; zbMATH DE number 61849