Test de différence de contrastes et somme pondérée de khi-deux

Samuel Bayomog (1) , Cécile Hardouin (1, 2) , Xavier Guyon (1) , Jian-Feng Yao (1, 3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 MODAL'X - Modélisation aléatoire de Paris X
3 IRMAR - Institut de Recherche Mathématique de Rennes

After recalling the framework of minimum-contrast estimation, its consistency and its asymptotic normality, we highlight the fact that these results do not require any stationarity or ergodicity assumptions. The asymptotic distribution of the underlying contrast difference test is a weighted sum of independent chi-square variables having one degree of freedom each. We illustrate these results in three contexts: (1) a nonhomogeneous Markov chain with likelihood contrast; (2) a Markov field with coding, pseudolikelihood or likelihood contrasts; (3) a not necessarily Gaussian time series with Whittle's contrast. In contexts (2) and (3), we compare experimentally the power of the likelihood-ratio test with those of other contrast-difference tests

Mots clés: Minimum-contrast estimation; contrast-difference test; inhomogeneous Markov chain; coding; conditional pseudolikelihood; Whittle's contrast

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Samuel Bayomog, Cécile Hardouin, Xavier Guyon, Jian-Feng Yao. Test de différence de contrastes et somme pondérée de khi-deux. Canadian Journal of Statistics, 1996, 24 (1), pp.115-130. ⟨hal-00110633⟩