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

Abstract

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 stationary 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 the other contrast-difference tests.