Computationally efficient approximations for independence tests in non-parametric regression

Abstract

) are independent random vectors with common joint probability density functionwhere f X and f ε are (univariate) probability density functions, f X is positive continuosly differentiable on S, and is a bounded measurable function satisfying(A.1) ε 1 , . . . , ε n are IID random variables with zero mean, unit variance, E(ε 4 j ) < ∞ and characteristic function c ε (t), t ∈ R.(A.2) X 1 , . . . , X n are IID random variables taking values on a compact support S, with common positive continuously differentiable density f X and characteristic function c X (t), t ∈ R.