How to determine the bandwidth of some nonlinear smoothers in practice

A nonlinear smoothing procedure which estimates a regression curve is proposed. A kernel operates on data which are first transformed in the way which is familiar in the theory of M-estimators. The bandwidth of the kernel is chosen by a “crossvalidatory” device and asymptotic optimality properties are proven. The proposed method is compared with AIC and FPE and shown to be asymptotically equivalent. An application to Raman-Spectra and a Monte Carlo study show how well our method works in practice.

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