Open Access
2009 Dimension reduction and variable selection in case control studies via regularized likelihood optimization
Florentina Bunea, Adrian Barbu
Electron. J. Statist. 3: 1257-1287 (2009). DOI: 10.1214/09-EJS537


Dimension reduction and variable selection are performed routinely in case-control studies, but the literature on the theoretical aspects of the resulting estimates is scarce. We bring our contribution to this literature by studying estimators obtained via 1 penalized likelihood optimization. We show that the optimizers of the 1 penalized retrospective likelihood coincide with the optimizers of the 1 penalized prospective likelihood. This extends the results of Prentice and Pyke (1979), obtained for non-regularized likelihoods. We establish both the sup-norm consistency of the odds ratio, after model selection, and the consistency of subset selection of our estimators. The novelty of our theoretical results consists in the study of these properties under the case-control sampling scheme. Our results hold for selection performed over a large collection of candidate variables, with cardinality allowed to depend and be greater than the sample size. We complement our theoretical results with a novel approach of determining data driven tuning parameters, based on the bisection method. The resulting procedure offers significant computational savings when compared with grid search based methods. All our numerical experiments support strongly our theoretical findings.


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Florentina Bunea. Adrian Barbu. "Dimension reduction and variable selection in case control studies via regularized likelihood optimization." Electron. J. Statist. 3 1257 - 1287, 2009.


Published: 2009
First available in Project Euclid: 4 December 2009

zbMATH: 1326.62161
MathSciNet: MR2566187
Digital Object Identifier: 10.1214/09-EJS537

Primary: 62J12
Secondary: 62J07 , 62K99

Keywords: bisection method , Case-control studies , Dimension reduction , Lasso , logistic regression , Model selection , prospective sampling , regularization , retrospective sampling

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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