We prove a CLT for empirical sums of a conditionally centred functional of a MRF on a non necessarly regular set of site. Since positive definiteness of the variance of the sums is crucial, we introduce the notion of conditionally separating partition and we give tools to verify such a positive definiteness. Exemples of Ising and gaussian MRF are studied.
Publié le : 2004-07-05
Classification:
Central Limit Theorem,
Markov random field,
Ising model,
Gaussian field,
conditionally centred functional,
irregular lattice,
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],
[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
@article{hal-00272423,
author = {Gaetan, Carlo and Guyon, Xavier},
title = {Central Limit Theorem for a conditionally centred functional of a Markov random field},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00272423}
}
Gaetan, Carlo; Guyon, Xavier. Central Limit Theorem for a conditionally centred functional of a Markov random field. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00272423/