Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it completely, we use density as a threshold to...

An essential problem in nonparametric smoothing of noisy data is a proper choice of the bandwidth or window width, which depends on a smoothing parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$k$$</EquationSource> </InlineEquation>. One way to choose <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$k$$</EquationSource> </InlineEquation> based on the data is leave-one-out-cross-validation. The selection of the cross-validation criterion is...</equationsource></inlineequation></equationsource></inlineequation>