A-dependence statistics for mutual and serial independence of categorical variables

Martin Bilodeau (1) , Pierre Lafaye de Micheaux (2, 3)

1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 GIN - Grenoble Institut des Neurosciences
3 SAGAG - Statistique Appliquée et de Géométrie Aléatoire de Grenoble

The Möbius transformation of probability cells in a multi-way contingency table is used to partition the Pearson chi-square test of mutual independence into A-dependence statistics. A similar partition is proposed for a universal and consistent test of serial independence in a stationary sequence of a categorical variable. The partition proposed can be adapted whether using estimated or theoretical marginal probabilities. With the aim of detecting a dependence of high order in a long sequence, A-dependence terms of the partition measuring increasing lagged dependences can be combined in a Box-Pierce type test of serial independence. A real data analysis of a nucleotides sequence using the Box-Pierce type test is provided.

Mots clés: Categorical variables; Chi-square tests; Mutual independence; Serial independence

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Martin Bilodeau, Pierre Lafaye de Micheaux. A-dependence statistics for mutual and serial independence of categorical variables. Journal of Statistical Planning and Inference, 2009, 139 (7), pp.2407-2419. ⟨10.1016/j.jspi.2008.11.006⟩. ⟨hal-00851018⟩