SFB 303 Discussion Paper No. A - 239
Author:
Härdle, Wolfgang, and Michael Nussbaum
Title: Kernel Estimation: The Equivalent Spline Smoothing Method
Abstract: Among nonparametric smoothers, there is a well-known correspondence
between kernel and Fourier series methods, pivoted by the Fourier
transform of the kernel. We establish a similar analytic correspondence
between kernel and spline estimators. Silverman's (1984) result on the
effective kernel for the classical Reinsch-Schoenberg smoothing spline
appears as a special case. The methods are used to obtain a Gaussian
approximation for this extended class of smoothing splines in a
nonparametric regression model. Asymptotic risk optimality of adaptive
bandwidth choice under nonnormal errors follows. This in particular applies
to Speckman's (1985) minimax linear smoothing spline, which thus attains a
recently established overall minimax bound.
Keywords: Kernel estimator, spline smoothing, variable bandwidth, filtering
coefficients, Gaussian approximation, adaptive bandwidth choice, asymptotic
minimax spline.
JEL-Classification-Number:
Creation-Date: May 1989
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