An estimation method for the chi-square divergence with application to test of hypotheses

Michel Broniatowski (1) , Samantha Leorato (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 SEFeMeQ - Dipartimento di Studi Economico-Finanziari e Metodi Quantitativi

We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the χ² is well suited both for the classical applications of the χ² for the analysis of contingency tables and for the statistical tests for parametric models, for which it has been advocated to be robust against inliers. We present two applications in testing. In the first one we deal with tests for finite and infinite numbers of linear constraints, while, in the second one, we apply χ²-methodology for parametric testing against contamination.

Mots clés: Chi-square divergence; Hypothesis testing; Linear constraints; Marginal distributions; Contamination models; Fenchel-Legendre transform; Inliers

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

Michel Broniatowski, Samantha Leorato. An estimation method for the chi-square divergence with application to test of hypotheses. Journal of Multivariate Analysis, 2016, 97 (6), pp.409-1436. ⟨hal-00555139⟩