Asymptotic optimality of likelihood-based cross-validation

Statistical Applications in Genetics and Molecular Biology
Mark J van der LaanSunduz Keles

Abstract

Likelihood-based cross-validation is a statistical tool for selecting a density estimate based on n i.i.d. observations from the true density among a collection of candidate density estimators. General examples are the selection of a model indexing a maximum likelihood estimator, and the selection of a bandwidth indexing a nonparametric (e.g. kernel) density estimator. In this article, we establish a finite sample result for a general class of likelihood-based cross-validation procedures (as indexed by the type of sample splitting used, e.g. V-fold cross-validation). This result implies that the cross-validation selector performs asymptotically as well (w.r.t. to the Kullback-Leibler distance to the true density) as a benchmark model selector which is optimal for each given dataset and depends on the true density. Crucial conditions of our theorem are that the size of the validation sample converges to infinity, which excludes leave-one-out cross-validation, and that the candidate density estimates are bounded away from zero and infinity. We illustrate these asymptotic results and the practical performance of likelihood-based cross-validation for the purpose of bandwidth selection with a simulation study. Moreover, we use likel...Continue Reading

Citations

Nov 2, 2007·BMC Evolutionary Biology·Yan ZhouHervé Philippe
Mar 12, 2008·Genetic Epidemiology·Alexandre BureauChantal Mérette
Oct 8, 2011·Biometrics·Iván Díaz Muñoz, Mark van der Laan
Dec 10, 2014·Statistics in Medicine·Romain NeugebauerSebastian Schneeweiss
Feb 19, 2014·Statistics in Medicine·Romain NeugebauerMark J van der Laan
Jul 17, 2013·Journal of Clinical Epidemiology·Romain NeugebauerPatrick J O'Connor
May 6, 2014·Brain Stimulation·Stefan M GoetzAngel V Peterchev
Feb 12, 2014·The International Journal of Biostatistics·Mark J van der Laan
Apr 8, 2015·The International Journal of Biostatistics·Daniel CommengesBenoit Liquet
Oct 13, 2017·The International Journal of Biostatistics·Mark van der Laan
Sep 20, 2018·Biometrics·Chunling Lu, Yuhong Yang
Nov 20, 2013·The International Journal of Biostatistics·Iván Díaz, Mark J van der Laan
Oct 28, 2019·Journal of the American Statistical Association·David BenkeserMarco Carone
Aug 14, 2020·The International Journal of Biostatistics·David BenkeserMark J van der Laan
Aug 15, 2014·Journal of Acquired Immune Deficiency Syndromes : JAIDS·Maya PetersenMatthias Egger

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