Testing independence in high dimensions
Let \((X_ 0,Y_ 0),...,(X_ n,Y_ n)\) be independent copies of some bivariate random vector (X,Y). Denote with \(f_ n\) and \(f^ 1_ n,f^ 2_ n\) bivariate and marginal kernel density estimators of the joint and marginal densities, respectively, computed from \((X_ i,Y_ i)\), \(1\leq i\leq n.\) A test for independence of X and Y is proposed which is based on a comparison of \(f_ n(X_ 0,Y_ 0)\) and \(f^ 1_ n(X_ 0)f^ 2_ n(Y_ 0)\). The paper also contains some power investigations for certain local alternatives which may be expressed in terms of densities.
scientific article; zbMATH DE number 4205640
scientific article