Penalized regression with model-based penalties

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Penalized regression with model-based penalties

TitlePenalized regression with model-based penalties
Publication TypeJournal Article
Year of Publication2000
AuthorsHeckman, NE, Ramsay, JO
JournalCANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
Volume28
Pagination241-258
Date PublishedJUN
Type of ArticleArticle
ISSN0319-5724
Keywordsnonparametric regression, penalized least squares, splines
AbstractNonparametric 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'')(2). Since integral>(*) over bar *(mu'')(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'')(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's. They also suggest a method for the estimation of L. They study their estimates via simulation and apply them to several data sets.
DOI10.2307/3315976