Testing independence of random vectors by inverse regressions

Jean Gérard Aghoukeng Jiofack (1) , Guy Martial Nkiet (2)

1 Département de Mathématiques [Yaoundé I] = Department of Mathematics [Yaoundé, Cameroon]
2 URMI - Unité de recherche en mathématiques et informatique [Université des Sciences et Techniques de Masuku]

We propose a new test of independence of random vectors. We first show that the null hypothesis implies the nullity of the trace of an operator involving inverse regressions covariance operators. Then, using an approach based on slicing, we define a test statistic for which an asymptotic distribution under null hypothesis is derived. Simulations that permit to evaluate the performance of the proposed test with comparisons with existing methods are given.

Mots clés: independence test; sliced inverse regression; consistency

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

Jean Gérard Aghoukeng Jiofack, Guy Martial Nkiet. Testing independence of random vectors by inverse regressions. 2011. ⟨hal-00614310v2⟩