Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/230816 
Year of Publication: 
2020
Series/Report no.: 
IRTG 1792 Discussion Paper No. 2020-010
Publisher: 
Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series", Berlin
Abstract: 
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.
Subjects: 
Kernel estimator
spline smoothing
filtering coefficients
differential operator
Green's function approximation
asymptotic minimax spline
JEL: 
C00
Document Type: 
Working Paper

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.