Multiple temporal cluster detection test using exponential inequalities

Christophe Demattei (1) , Nicolas Molinari (1)

1 AIDMP - Aide à la Décision pour une Médecine Personnalisé - Laboratoire de Biostatistique, Epidémiologie et Recherche Clinique - EA 2415

The method of Molinari et al. (2001) is a multiple temporal cluster detection approach, which is based on a data transformation. The model selection procedure and the test of the cluster significance are achieved by bootstrap. The use of simulations is a common point between existing temporal cluster detection methods. The aim of this paper is to propose a new approach to avoid the use of such simulations in the cluster significance test stage. A direct application of the Bernstein inequality allows to compute upper bounds for $p$-values for each potential cluster. We also propose another model selection procedure based on multiple structural changes developed by Bai and Perron (1998). The new detection approach based on inequalities is detailed. Those inequalities are applied on simulated data and on two real data set. A discussion concludes the paper.

Mots clés: Cluster detection; Bernstein inequality; Multiple structural changes; Temporal cluster; Break dates; Double maximum test

Domaines: Statistiques [math.ST]

Christophe Demattei, Nicolas Molinari. Multiple temporal cluster detection test using exponential inequalities. Far East Journal of Theoretical Statistics, 2006, 19, pp.231-244. ⟨hal-00134501⟩