Open Access
August 2001 A General Projection Framework for Constrained Smoothing
E. Mammen, J. S. Marron, B. A. Turlach, M. P. Wand
Statist. Sci. 16(3): 232-248 (August 2001). DOI: 10.1214/ss/1009213727


There are a wide array of smoothing methods available for finding structure in data. A general framework is developed which shows that many of these can be viewed as a projection of the data, with respect to appropriate norms. The underlying vector space is an unusually large product space, which allows inclusion of a wide range of smoothers in our setup (including many methods not typically considered to be projections). We give several applications of this simple geometric interpretation of smoothing. A major payoff is the natural and computationally frugal incorporation of constraints. Our point of view also motivates new estimates and helps understand the finite sample and asymptotic behavior of these estimates.


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E. Mammen. J. S. Marron. B. A. Turlach. M. P. Wand. "A General Projection Framework for Constrained Smoothing." Statist. Sci. 16 (3) 232 - 248, August 2001.


Published: August 2001
First available in Project Euclid: 24 December 2001

zbMATH: 1059.62535
MathSciNet: MR1874153
Digital Object Identifier: 10.1214/ss/1009213727

Keywords: Additive models , constrained smoothing , kernel smoothing , local polynomials , monotone smoothing , smoothing splines

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.16 • No. 3 • August 2001
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