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
Date PublishedJUN
Type of ArticleArticle
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.