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Empirical functionals and efficient smoothing parameter selection. (With discussion). (English) Zbl 0786.62050

A main difficulty in nonparametric estimation of curves such as densities, spectra and regression functions is an appropriate choice of a smoothing parameter, regularization parameter or bandwidth. This difficulty is quantified by nonparametric information bounds. Asymptotically efficient estimators which attain these bounds are constructed. They turn out to be substantially less variable than cross- validation and other selection procedures and may offer improvements at moderate sample sizes. The paper is followed by an extensive discussion (23 contributions) and a rejoinder by the authors.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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