Summary
Let Y be a Markov random field 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.
Résumé
Soit Y un champ de Markov sur S, paramétrisé via ses spécifications conditionnelles locales. On étudie la consistance des estimateurs de codage et de pseudo-vraisemblance. Nous obtenons alors la normalité asymptotique conditionnelle pour l’estimateur de codage et en déduisons que le test asymptotique de différence de codage pour deux hypothèses emboîtées est une statistique du chi 2. Pour établir ces résultats, il n’est pas nécessaire de supposer le lattice S régulier ni la spécification invariante par translation ni le champ Y faiblement dépendant.
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© 1992 Springer-Verlag Berlin Heidelberg
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Guyon, X., Hardouin, C. (1992). The Chi-Square Coding Test for Nested Markov Random Field Hypotheses. In: Barone, P., Frigessi, A., Piccioni, M. (eds) Stochastic Models, Statistical Methods, and Algorithms in Image Analysis. Lecture Notes in Statistics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2920-9_11
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DOI: https://doi.org/10.1007/978-1-4612-2920-9_11
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