The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals.
Attention is focused on local polynomial smoothers.
Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic bandwidth selectors for estimating both the mean and variance functions.