Nonlinear canonical analysis and independence tests

Abstract

Measures of association between two random variables (r.v.) that are symmetric nondecreasing functions of the canonical coefficients provided by the nonlinear canonical analysis of the r.v.'s are studied. These measures can be used to characterize independence. Their estimators are obtained by estimating a suitable approximation to nonlinear canonical analysis. When some conditions ae satisfied, asymptotic distributions of the estimators, both under the independence hypothesis and under dependence, are given. A class of tests of independence with asymptotic level of significance can be investigated.