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Linear minimax efficiency of local polynomial regression smoothers. (English) Zbl 1025.62017
Summary: This paper proves that local polynomial regression smoothers achieve linear minimax efficiency over a class of functions, generalizing a result of J. Fan [Ann. Stat. 21, 196-216 (1993; Zbl 0773.62029)] for local linear smoothers and proving that a conjecture of J. Fan and I. Gijbels [Local polynomial modelling and its applications. (1996; Zbl 0873.62037)] is true. Consequences are also illustrated.

MSC:
62G08 Nonparametric regression and quantile regression
62J02 General nonlinear regression
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