Asymptotic Properties of Adaptive Group Lasso in High-Dimensional Generalized Additive Model with a Diverging Number of Parameters and Consistent Tuning Parameter Selection

• Activity Number: 183 - Contributed Poster Presentations: IMS
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Kaixu Yang* and Jun Liu
• Companies: and Michigan State University
• Keywords: generalized additive model; high dimensional; variable selection; tuning parameter selection; adaptive group lasso

Abstract

Generalized additive models with exponential family distributions are considered in the high dimension set up with a diverging number of parameters. The variable selection is performed in two steps. The first step applies group lasso on the expanded bases of the functions and is showed to be able to select all nonzero functions and not to over-select too much. The second step uses adaptive group lasso with the weights from the group lasso estimator. We showed that with a good initial estimator (ex. the group lasso estimator), the adaptive group lasso achieves selection consistency. The rates of convergence of both steps are also derived. Tuning parameter selection is also discussed. We showed that the generalized information criterion (GIC) is able to select a tuning parameter that makes perfect variable selection asymptotically.