We investigate the extension of binning methodology to fast computation of several auxiliary quantities that arise in local polynomial smoothing. Examples include degrees of freedom measures, cross-validation functions, variance estimates and exact measures of error. It is shown that the...

The typical generalized linear model for a regression of a response Y on predictors (X,Z) has conditional mean function based upon a linear combination of (X,Z). We generalize these models to have a nonparametric component, replacing the linear combination $\alpha_0^T X + \beta_0^T Z$ by...

The accuracy of the binned kernel density estimator is studied for general binning rules. We derive mean squared error results for the closeness of this estimator to both the true density and the unbinned kernel estimator. The binning rule and smoothness of the kernel function are shown to...

The most important parameter of a histogram is the bin width, since it controls the trade-off between presenting a picture with too much detail (``undersmoothing'') or too little detail (``oversmoothing'') with respect to the true distribution. Despite this importance there has been surprisingly...

Virtually all common bandwidth selection algorithms are based on a certain type of kernel functional estimator. Such estimators can be very computationally expensive, so in practice they are often replaced by fast binned approximations. This is especially worthwhile when the bandwidth selection...