Corrected generalized cross-validation for finite ensembles of penalized estimators

arXiv:2310.01374v2 Announce Type: replace-cross
Abstract: Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the prediction risk of arbitrary ensembles of penalized least-squares estimators. We show that GCV is inconsistent for any finite ensemble of size greater than one. Towards repairing this shortcoming, we identify a correction …

abstract arxiv error freedom generalized math.st paper prediction risk sample sense stat.me stat.ml stat.th training type validation