Abstract
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.