A robust test for homoscedasticity in nonparametric regression

Abstract

We consider a nonparametric location scale model and propose a new test for homoscedasticity (constant scale function). The test is based on an estimate of a deterministic function that vanishes if and only if the hypothesis of a constant scale function is satisfied and an empirical process estimating this function is investigated. Weak convergence to a scaled Brownian bridge is established, which allows a simple calculation of critical values. The new test can detect alternatives converging to the null hypothesis at a rate n −1/2 and is robust with respect to the presence of outliers. The finite sample properties are investigated by means of a simulation study, and the test is compared with some nonrobust tests for a constant scale function, which have recently been proposed in the literature.