Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional...

Theories of nonparametric regression are usually based on the assumption that the design density exists. However, in some applications such as those involving high-dimensional or chaotic time series data, the design measure may be singular and may be likely to have a fractal (nonintegral)...