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.
Publié le : 2004-12-14
Classification:
C_p,
generalized maximum likelihood,
extended exponential criterion,
geometry,
bias,
variability,
curvature,
62G08,
62G20
@article{1107794875,
author = {Kou, S. C.},
title = {From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 2444-2468},
language = {en},
url = {http://dml.mathdoc.fr/item/1107794875}
}
Kou, S. C. From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression. Ann. Statist., Tome 32 (2004) no. 1, pp. 2444-2468. http://gdmltest.u-ga.fr/item/1107794875/