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Lasso with convex loss: Model selection consistency and estimation

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  • Wojciech Rejchel

Abstract

Variable selection is a fundamental challenge in statistical learning if one works with data sets containing huge amount of predictors. In this artical we consider procedures popular in model selection: Lasso and adaptive Lasso. Our goal is to investigate properties of estimators based on minimization of Lasso-type penalized empirical risk with a convex loss function, in particular nondifferentiable. We obtain theorems concerning rate of convergence in estimation, consistency in model selection and oracle properties for Lasso estimators if the number of predictors is fixed, i.e. it does not depend on the sample size. Moreover, we study properties of Lasso and adaptive Lasso estimators on simulated and real data sets.

Suggested Citation

  • Wojciech Rejchel, 2016. "Lasso with convex loss: Model selection consistency and estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(7), pages 1989-2004, April.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:7:p:1989-2004
    DOI: 10.1080/03610926.2013.870799
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