From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression
Abstract
Description
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.
Published at http://dx.doi.org/10.1214/009053604000000841 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Published at http://dx.doi.org/10.1214/009053604000000841 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)