Statistics
P-value calculations for multiple temporal cluster detection
Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 697-701.

The aim of this Note is to propose a new approach to test multiple temporal cluster significance. Our method is based on a data transformation and on multiple structural change models, and it completes a former method (Molinari et al., 2001). Instead of using bootstrap replicates, we compute upper bounds for p-values using the Bernstein inequality. The inequalities on which the new detection method is based are detailed.

L'objectif de cette Note est de proposer une nouvelle approche afin de tester la significativité de clusters temporaux multiples. Notre approche, qui est basée sur une transformation des données et sur des modèles de changements structurels multiples, complète une méthode existante (Molinari et al., 2001). Au lieu d'utiliser des simulations par bootstrap, nous calculons des bornes supérieures pour les p-valeurs en utilisant l'inégalité de Bernstein. Les inégalités servant de base à la nouvelle méthode de détection sont détaillées.

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Published online:
DOI: 10.1016/j.crma.2007.04.004
Dematteï, Christophe 1; Molinari, Nicolas 1

1 Laboratoire de biostatistique, institut universitaire de recherche clinique, 641, avenue du Doyen Gaston-Giraud, 34093 Montpellier, France
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Dematteï, Christophe; Molinari, Nicolas. P-value calculations for multiple temporal cluster detection. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 697-701. doi : 10.1016/j.crma.2007.04.004. http://www.numdam.org/articles/10.1016/j.crma.2007.04.004/

[1] Bai, J.; Perron, P. Computation and analysis of multiple structural change models, J. Applied Econometrics, Volume 18 (2003), pp. 1-22

[2] Bernstein, S. The Theory of Probabilities, Gostehizdat Publishing House, Moscow, 1946

[3] C. Bonaldi, Analyse de clusters sur le temps, Thesis, University of Montpellier I, Montpellier, 2003

[4] Kulldorff, M. A spatial scan statistic, Communications in Statistics—Theory and Methods, Volume 26 (1997), pp. 1481-1496

[5] Kulldorff, M.; Nagarwalla, N. Spatial disease clusters: detection and inference, Statistics in Medicine, Volume 14 (1995), pp. 799-810

[6] Molinari, N.; Bonaldi, C.; Daurès, J.P. Multiple temporal cluster detection, Biometrics, Volume 57 (2001), pp. 577-583

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