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A central limit theorem for conditionally centred random fields with an application to Markov fields

Part of: Inference from stochastic processes Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Francis Comets  and
Martin Janžura
Francis Comets*
Affiliation:
Université Paris 7
Martin Janžura*
Affiliation:
Academy of Sciences, Prague
*
∗Postal address: Université Paris 7 – Denis Diderot, Mathématiques, case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France. Email address: [email protected].
∗∗Postal address: Institute of Information Theory and Automation, Academy of Sciences, Pod vodárenskou věží 4, CZ – 182 08 Praha, Czech Republic.
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Abstract

We prove a central limit theorem for conditionally centred random fields, under a moment condition and strict positivity of the empirical variance per observation. We use a random normalization, which fits non-stationary situations. The theorem applies directly to Markov random fields, including the cases of phase transition and lack of stationarity. One consequence is the asymptotic normality of the maximum pseudo-likelihood estimator for Markov fields in complete generality.

Keywords

Central limit theoremMarkov random fieldsconditional centring

MSC classification

Primary: 60G60: Random fields
Secondary: 60F05: Central limit and other weak theorems 62M40: Random fields; image analysis
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 608 - 621
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Unité de Recherche Associée CNRS 1321 ‘Statistique et Modèles Aléatoires’.

Supported by GA ČR Grant No. 202/93/0449.

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