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.
Creation-Date: May 1989
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