  Heteroskedastic errors can lead to inaccurate statistical conclusions if they
are not properly handled. We introduce a test for heteroskedasticity for the
nonparametric regression model with multiple covariates. It is based on a
suitable residual-based empirical distribution function. The residuals are
constructed using local polynomial smoothing. Our test statistic involves a
detection function that can verify heteroskedasticity by exploiting just the
independence-dependence structure between the detection function and model
errors, i.e. we do not require a specific model of the variance function. The
procedure is asymptotically distribution free: inferences made from it do not
depend on unknown parameters. It is consistent at the parametric (root-n) rate
of convergence. Our results are extended to the case of missing responses and
illustrated with simulations.
