caa a22 4500 37892592X CHVBK 20180305123617.0 cr unu---uuuuu 161128e20040322xx s 000 0 eng 10.2202/1544-6115.1036 doi (NATIONALLICENCE)gruyter-10.2202/1544-6115.1036 Asymptotic Optimality of Likelihood-Based Cross-Validation [Elektronische Daten] [Mark J. van der Laan, Sandrine Dudoit, Sunduz Keles] 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 likelihood-based cross-validation in the context of regulatory motif detection in DNA sequences. ©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston Statistical Theory and Methods nationallicence Likelihood cross-validation nationallicence maximum likelihood estimation nationallicence Kullback-Leibler divergence nationallicence density estimation nationallicence bandwidth selection nationallicence model selection nationallicence variable selection nationallicence van der Laan Mark J. Division of Biostatistics, School of Public Health, University of California, Berkeley aut Dudoit Sandrine Division of Biostatistics, School of Public Health, University of California, Berkeley aut Keles Sunduz Division of Biostatistics, School of Public Health, University of California, Berkeley aut Statistical Applications in Genetics and Molecular Biology De Gruyter 3/1(2004-03-22), 1-23 3:1<1 2004 3 sagmb https://doi.org/10.2202/1544-6115.1036 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2202/1544-6115.1036 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- van der Laan Mark J. Division of Biostatistics, School of Public Health, University of California, Berkeley aut NATIONALLICENCE 700 1- Dudoit Sandrine Division of Biostatistics, School of Public Health, University of California, Berkeley aut NATIONALLICENCE 700 1- Keles Sunduz Division of Biostatistics, School of Public Health, University of California, Berkeley aut NATIONALLICENCE 773 0- Statistical Applications in Genetics and Molecular Biology De Gruyter 3/1(2004-03-22), 1-23 3:1<1 2004 3 sagmb CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter