Higher Order Correlation coefficients

René Blacher (1)

1 IPS - Inférence Processus Stochastiques

We continue the study of higher order correlation coefficients. These coefficients complement the classical correlation coefficient by measuring some dependences more and more sharply. We prove that they can detect the existence of functional dependence of type $g(X)=g'(Y)$. We obtain the asymptotic distribution of empirical higher order correlation coefficients.

Mots clés: Correlation coefficients; canonical analysis; functional dependence; conditional probability; orthogonal functions; Hilbertian test

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

René Blacher. Higher Order Correlation coefficients. [Research Report] LJK. 2012. ⟨hal-00734568⟩