Testing the Hypothesis of a Homoscedastic Error Term in Simple,Nonparametric Regression

Abstract

Consider the nonparametric regression model Y = m(X)+ τ(X)ε, where X and ε are independent random variables, ε has a median of zero and variance σ², 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. This article considers the problem of testing H ₀:τ = 1, the hypothesis that the error term is homoscedastic. Several methods were considered, two of which were found that control the probability of a Type I error well in simulations. One is fast from a computational point of view, and the other is based in part on a bootstrap method. Neither dominates in terms of power.