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by Zhen Luo, Zhen Luo, Grace Wahba, Grace Wahba
Journal of the American Statistical Association
ftp://ftp.stat.wisc.edu/pub/wahba/has.ps
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Abstract:
Abstract. An adaptive spline method for smoothing is proposed which combines features from both regression spline and smoothing spline approaches. One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous "curvature " of true functions at different locations. This method can be applied to many multivariate function estimation problems, which is illustrated in this paper by an application to smoothing temperature data on the globe. The performance of this method in a simulation study is found to be comparable to the Wavelet Shrinkage methods proposed by Donoho and Johnstone. The problem of how to count the degrees of freedom for an adaptively chosen set of basis functions is addressed. This issue arises also in the MARS procedure proposed by Friedman and other adaptive regression spline procedures. Key words and phrases: Smoothing, spatial adaptability, splines, stepwise regression, the
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