Kernel Estimation: the Equivalent Spline Smoothing Method

Wolfgang Härdle and Michael Nussbaum

No 2020-010, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

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.

Keywords: Kernel estimator; spline smoothing; filtering coefficients; differential operator; Green's function approximation; asymptotic minimax spline (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-ecm
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Related works:
Working Paper: Kernel Estimation: the Equivalent Spline-Smoothing Method (1994)
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2020010

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