Selection of tuning parameters in bridge regression models via Bayesian information criterion

2012/03/31 by Shuichi Kawano
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian information criterion #Bayesian linear regression #Bayesian probability #Bridge (graph theory) #Model selection #Regression #Regression analysis #Selection (genetic algorithm) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #msc:62F15 #msc:62G05 #msc:62J05 #stat.ME #stat.ML

paper · pdf · doi:10.1007/s00362-013-0561-7

published as Statistical Papers 55 (2014) 1207-1223 · 20 pages, 5 figures

arxiv created 2012/04/14 · openalex publication_date 2013/10/14 · arxiv updated 2015/02/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be viewed as a model selection and evaluation problem. We propose a model selection criterion for evaluating bridge regression models in terms of Bayesian approach. This selection criterion enables us to select the adjusted parameters objectively. We investigate the effectiveness of our proposed modeling strategy through some numerical examples.

Citations

• Further analysis of the data by Akaike's information criterion and the finite corrections
• Nearly unbiased variable selection under minimax concave penalty
• Regression and time series model selection in small samples
• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• One-step sparse estimates in nonconcave penalized likelihood models
• A Statistical View of Some Chemometrics Regression Tools
• Penalized Regressions: The Bridge versus the Lasso
• A new look at the statistical model identification
• Smoothing noisy data with spline functions
• Ridge Regression: Biased Estimation for Nonorthogonal Problems