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December 2004 From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression
S. C. Kou
Ann. Statist. 32(6): 2444-2468 (December 2004). DOI: 10.1214/009053604000000841

Abstract

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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S. C. Kou. "From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression." Ann. Statist. 32 (6) 2444 - 2468, December 2004. https://doi.org/10.1214/009053604000000841

Information

Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1076.62039
MathSciNet: MR2153991
Digital Object Identifier: 10.1214/009053604000000841

Subjects:
Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 6 • December 2004
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