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.
Publié le : 2001-08-14
Classification:
Kernel smoothing,
local polynomials,
smoothing splines,
constrained smoothing,
monotone smoothing,
additive models
@article{1009213727,
author = {Mammen, E. and Marron, J. S. and Turlach, B. A. and Wand, M. P.},
title = {A General Projection Framework for Constrained Smoothing},
journal = {Statist. Sci.},
volume = {16},
number = {2},
year = {2001},
pages = { 232-248},
language = {en},
url = {http://dml.mathdoc.fr/item/1009213727}
}
Mammen, E.; Marron, J. S.; Turlach, B. A.; Wand, M. P. A General Projection Framework for Constrained Smoothing. Statist. Sci., Tome 16 (2001) no. 2, pp. 232-248. http://gdmltest.u-ga.fr/item/1009213727/