%0 Journal Article
%T From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression
%A S. C. Kou
%J Mathematics
%D 2005
%I arXiv
%R 10.1214/009053604000000841
%X This paper studies, under the setting of spline regression, the connection between finite-sample properties of selection criteria and their asymptotic counterparts, focusing on bridging the gap between the two. We introduce a bias-variance decomposition of the prediction error, using which it is shown that in the asymptotics the bias term dominates the variability term, providing an explanation of the gap. A geometric exposition is provided for intuitive understanding. The theoretical and geometric results are illustrated through a numerical example.
%U http://arxiv.org/abs/math/0508596v1