Open Access
August 2012 The log-linear group-lasso estimator and its asymptotic properties
Yuval Nardi, Alessandro Rinaldo
Bernoulli 18(3): 945-974 (August 2012). DOI: 10.3150/11-BEJ364

Abstract

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-linear model using the blocks of nonzero coefficients recovered by the group-lasso procedure. We investigate the asymptotic properties of the group-lasso estimator as a model selection method in a double-asymptotic framework, in which both the sample size and the model complexity grow simultaneously. We provide conditions guaranteeing that the group-lasso estimator is model selection consistent, in the sense that, with overwhelming probability as the sample size increases, it correctly identifies all the sets of nonzero interactions among the variables. Provided the sequences of true underlying models is sparse enough, recovery is possible even if the number of cells grows larger than the sample size. Finally, we derive some central limit type of results for the log-linear group-lasso estimator.

Citation

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Yuval Nardi. Alessandro Rinaldo. "The log-linear group-lasso estimator and its asymptotic properties." Bernoulli 18 (3) 945 - 974, August 2012. https://doi.org/10.3150/11-BEJ364

Information

Published: August 2012
First available in Project Euclid: 28 June 2012

zbMATH: 1243.62107
MathSciNet: MR2948908
Digital Object Identifier: 10.3150/11-BEJ364

Keywords: consistency , group lasso , log-linear models , Model selection

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

Vol.18 • No. 3 • August 2012
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