Smoothing Techniques: With Implementation in S
The author has attempted to present a book that provides a non-technical introduction into the area of non-parametric density and regression function estimation. The application of these methods is discussed in terms of the S computing environment. Smoothing in high dimensions faces the problem of data sparseness. A principal feature of smoothing, the averaging of data points in a prescribed neighborhood, is not really practicable in dimensions greater than three if we have just one hundred data points. Additive models provide a way out of this dilemma; but, for their interactiveness and recursiveness, they require highly effective algorithms. For this purpose, the method of WARPing (Weighted Averaging using Rounded Points) is described in great detail.
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algorithm approximation ASE(h asymptotic average bandwidth h bias biased CV binmesh Binning the data binnumber binwidth Buffalo snowfall data calculate compute confidence band confidence intervals confidence limits corresponding counts cross-validation CV(h data set defined density function di(h double endfor Epanechnikov Epanechnikov kernel Equation estimated bias Exercise Figure formula frequency histogram Gaussian kernel golden section bootstrap grid Härdle Hence histogram integer k-NN estimate kernel density estimation kernel function kernelproc L2 norm linear maximum likelihood mh(x midpoints minimizing MISE optimal bandwidth Nadaraya-Watson estimate non-empty bins nonempty nonparametric normal distribution Note number of observations numbin Old Faithful geyser order statistics origin x0 penalizing functions plot points polygon Quartic kernel random numbers random variables result routine samples score function selector simulated smoothing parameter Squared Error statistics technique theorem unknown density variance vector WARPing density estimation WARPing estimate weighting function weighting the bins Whi(x ysum