Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$

The Annals of Statistics · 1985 · Volume 13 · Issue 3

Abstract

For nonparametric regression estimation on a bounded interval, optimal rates of decrease for integrated mean square error are known but not the best possible constants. A sharp result on such a constant, i.e., an analog of Fisher's bound for asymptotic variances is obtained for minimax risk over a Sobolev smoothness class. Normality of errors is assumed. The method is based on applying a recent result on minimax filtering in Hilbert space. A variant of spline smoothing is developed to deal with noncircular models.

Keywords

41A15, 62G05, 62G20, 65D10, asymptotic minimax risk, boundary effects, linear spline estimation, Smooth nonparametric regression

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