Asymptotic Optimality of Likelihood-Based Cross-Validation
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| 024 | 7 | 0 | |a 10.2202/1544-6115.1036 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.2202/1544-6115.1036 | ||
| 245 | 0 | 0 | |a Asymptotic Optimality of Likelihood-Based Cross-Validation |h [Elektronische Daten] |c [Mark J. van der Laan, Sandrine Dudoit, Sunduz Keles] |
| 520 | 3 | |a 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. | |
| 540 | |a ©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston | ||
| 690 | 7 | |a Statistical Theory and Methods |2 nationallicence | |
| 690 | 7 | |a Likelihood cross-validation |2 nationallicence | |
| 690 | 7 | |a maximum likelihood estimation |2 nationallicence | |
| 690 | 7 | |a Kullback-Leibler divergence |2 nationallicence | |
| 690 | 7 | |a density estimation |2 nationallicence | |
| 690 | 7 | |a bandwidth selection |2 nationallicence | |
| 690 | 7 | |a model selection |2 nationallicence | |
| 690 | 7 | |a variable selection |2 nationallicence | |
| 700 | 1 | |a van der Laan |D Mark J. |u Division of Biostatistics, School of Public Health, University of California, Berkeley |4 aut | |
| 700 | 1 | |a Dudoit |D Sandrine |u Division of Biostatistics, School of Public Health, University of California, Berkeley |4 aut | |
| 700 | 1 | |a Keles |D Sunduz |u Division of Biostatistics, School of Public Health, University of California, Berkeley |4 aut | |
| 773 | 0 | |t Statistical Applications in Genetics and Molecular Biology |d De Gruyter |g 3/1(2004-03-22), 1-23 |q 3:1<1 |1 2004 |2 3 |o sagmb | |
| 856 | 4 | 0 | |u https://doi.org/10.2202/1544-6115.1036 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.2202/1544-6115.1036 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a van der Laan |D Mark J. |u Division of Biostatistics, School of Public Health, University of California, Berkeley |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Dudoit |D Sandrine |u Division of Biostatistics, School of Public Health, University of California, Berkeley |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Keles |D Sunduz |u Division of Biostatistics, School of Public Health, University of California, Berkeley |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Statistical Applications in Genetics and Molecular Biology |d De Gruyter |g 3/1(2004-03-22), 1-23 |q 3:1<1 |1 2004 |2 3 |o sagmb | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||