Home > Open Access Journals > JMASM > Vol. 6 (2007) > Iss. 1

#### Article Title

#### Abstract

Consider the nonparametric regression model *Y = m(X) + τ(X)ε* , where *X* and *ε* are independent random variables, *ε* has a mean of zero and variance *σ ^{2}*,

*τ*is some unknown function used to model heteroscedasticity, and

*m(X)*is an unknown function reflecting some conditional measure of location associated with

*Y*, given

*X*. Detecting dependence, by testing the hypothesis that

*m(X)*does not vary with

*X*, has the potential of being more sensitive to a wider range of associations compared to using Pearson's correlation. This note has two goals. The first is to point out situations where a certain variation of an extant test of this hypothesis fails to control the probability of a Type I error, but another variation avoids this problem. The successful variation provides a new test of

*H*≡ 1, the hypothesis that the error term is homoscedastic, which has the potential of higher power versus a method recently studied by Wilcox (2006). The second goal is to report some simulation results on how this method performs.

_{0}:τ(X)