From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression

Details From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression

2005-08-30

arxiv.org/abs/math/0508596v1

Annals of Statistics 2004, Vol. 32, No. 6, 2444-2468

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000841 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000841

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.

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