JSM 2011 Online Program

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Abstract Details

 Activity Number: 83 Type: Contributed Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM Sponsor: IMS Abstract - #302084 Title: Group LASSO for High-Dimensional Sparse Quantile Regression Models Author(s): Kengo Kato*+ Companies: Hiroshima University Address: 1-3-1 Kagamiyama , Higashi-Hiroshima, International, 739-0014, Japan Keywords: additive model ; group Lasso ; non-asymptotic bound ; quantile regression Abstract: This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much larger than the sample size while the number of active'' variables is sufficiently small. We establish a non-asymptotic bound on the \ell_2 estimation error of the estimator. This bound explains situations under which the group Lasso estimator is potentially superior/inferior to the \ell_1 penalized quantile regression estimator. We also propose a data-dependent choice of the tuning parameter to make the method more practical, by extending the original proposal of Belloni and Chernozhukov (2011) for the \ell_1 penalized quantile regression estimator. As an application, we analyze high dimensional additive quantile regression models. We show that under a set of primitive regularity conditions, the group Lasso estimator can attain the convergence rate arbitrarily close to the oracle rate. Finally, we conduct simulations experiments to examine our theoretical results.

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