Deux procédures de détection de rupture pour des observations poissonniennes groupées

Dariush Ghorbanzadeh (1) , Rachid Lounès (2, 3)

1 CEDRIC - LAETITIA - CEDRIC. Traitement du signal et architectures électroniques
2 MAP5 - Mathématiques Appliquées à Paris 5
3 UPD5 Mathématiques Informatique - Université Paris Descartes - UFR de Mathématiques et Informatique

We consider two tests with regard to detection of change of parameter in a sequence of independent Poisson random variables. The first test considered is based on the likelihood ratio appropriately adapted for a change point problem. The limiting distribution of the test statistics, under the null hypothesis is evaluated by asymptotical techniques. Under the null hypothesis the distribution of the test statistic obtained by maximization of the likelihood ratio converges to the supremum of an square function of the Brownian bridge process. The second test use Bayes technic, and is based on the marginal posterior density of the change. Finaly, we apply the results for a set of data from the Liverpool Registry during 1960 to 1982, and compare the two procedures.

Mots clés: Change point; Penalized likelihood ratio test; brownian bridge; prior distribution; posterior distribution

Domaines: Applications [stat.AP]

Dariush Ghorbanzadeh, Rachid Lounès. Deux procédures de détection de rupture pour des observations poissonniennes groupées. Revue de Statistique Appliquée, 1996, XLIV (3), pp.47-61. ⟨hal-00459574⟩