TESTING HETEROSCEDASTICITY IN NONPARAMETRIC REGRESSION

The importance of being able to detect heteroscedasticity in regressio n is widely recognized because efficient inference for the regression function requires that heteroscedasticity is taken into account. In th is paper a simple consistent test for heteroscedasticity is proposed i n a nonparametric regression set-up. The test is based on an estimator for the best L-2-approximation of the variance function by a constant . Under mild assumptions asymptotic normality of the corresponding tes t statistic is established even under arbitrary fixed alternatives. Co nfidence intervals are obtained for a corresponding measure of heteros cedasticity. The finite sample performance and robustness of these pro cedures are investigated in a simulation study and Box-type correction s are suggested for small sample sizes.