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The chi-square coding test for nested Markov random field hypotheses
Cécile Hardouin1, Xavier Guyon1

Let Y be a Markov random foeld on S parametrized via its local conditional specifications. We study consistency of coding and pseudo-likelihood estimators. Then we obtain conditional asymptotic normality for the coding estimator and deduce that the difference of coding statistic for two nested hypotheses is, unconditionally, a chi-square. For these results, we do not need regularity of the lattice, translation invariance for the specification or weak dependence for the field.
1:  SAMOS - Statistique Appliquée et MOdélisation Stochastique
Conditional specification – Markov random field – coding and pseudo-likelihood estimators – difference of coding tests