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Härdle, Wolfgang Karl
Nussbaum, Michael
Year of Publication: 
Series/Report no.: 
IRTG 1792 Discussion Paper No. 2020-010
Among nonparametric smoothers, there is a well-known correspondence between kernel and Fourier series methods, pivoted by the Fourier transform of the kernel. This suggests a similar relationship between kernel and spline estimators. A known special case is the result of Silverman (1984) on the effective kernel for the classical Reinsch-Schoenberg smoothing spline in the nonparametric regression model. We present an extension by showing that a large class of kernel estimators have a spline equivalent, in the sense of identical asymptotic local behaviour of the weighting coefficients. This general class of spline smoothers includes also the minimax linear estimator over Sobolev ellipsoids. The analysis is carried out for piecewise linear splines and equidistant design.
Kernel estimator
spline smoothing
filtering coefficients
differential operator
Green's function approximation
asymptotic minimax spline
Document Type: 
Working Paper

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