Tuning Parameter Selection in Bridge Regression Modeling

• Activity Number: 191
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Shuichi Kawano*+
• Companies: Osaka Prefecture University
• Keywords: Bridge penalty ; Model selection ; Regularization ; Sparse regression

Abstract

Variable selection is fundamental in statistical modeling. A traditional technique for variable selection is the best subset or stepwise selection based on t-value, AIC or BIC, which has been the most familiar method. In recent years, some penalized estimation procedures for variable selection, such as lasso, elastic net, SCAD, and MCP, have received considerable attention. We, in particular, focus on the bridge regression, which is a regression model estimated by regularization with Lp penalty. Although various researches show that the bridge regression is useful, there remains a problem of evaluating the regression models, which leads to the selection of adjusted parameters involved in the constructed bridge regression models. In this talk, we introduce a model selection criterion for evaluating the models estimated by the penalized maximum likelihood method with Lp penalty from the viewpoint of Bayesian approach. The proposed criterion enables us to select appropriate values of adjusted parameters in the bridge regression models objectively. Through some simulation studies, we investigate the performance of our proposed methodology.