@article { ISI:000090039100002,
title = {Penalized regression with model-based penalties},
journal = {CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE},
volume = {28},
number = {2},
year = {2000},
month = {JUN},
pages = {241-258},
publisher = {CANADIAN JOURNAL STATISTICS},
type = {Article},
address = {675 DENBURY AVENUE, OTTAWA, ON K2A 2P2, CANADA},
abstract = {Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function integral mu based on observations t(i), Y-i is the minimizer of Sigma {Y-i - mu>(*) over bar * (t(i))}(2) + lambda integral>(*) over bar *(mu{\textquoteright}{\textquoteright})(2). Since integral>(*) over bar *(mu{\textquoteright}{\textquoteright})(2) is zero when mu is a line, the cubic smoothing spline estimate favors the parametric model mu>(*) over bar * (t) = alpha (0) + alpha (1)t. Here the authors consider replacing integral>(*) over bar *(mu{\textquoteright}{\textquoteright})(2) with the mon general expression integral>(*) over bar * (L mu)(2) where L is a linear differential operator with possibly nonconstant coefficients. The resulting estimate of mu performs well, particularly if L mu is small. They present an O(n) algorithm far the computation of mu. This algorithm is applicable to a wide class of L{\textquoteright}s. They also suggest a method for the estimation of L. They study their estimates via simulation and apply them to several data sets.},
keywords = {nonparametric regression, penalized least squares, splines},
issn = {0319-5724},
doi = {10.2307/3315976},
author = {Heckman, NE and Ramsay, JO}
}