Regularization Parameter Selections via Generalized Information Criterion

• 成果类型: Article
• 署名作者: Zhang, Yiyun; Li, Runze; Tsai, Chin-Ling
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Davis; Novartis; Novartis USA
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08013
• 发表日期: 2010
• 页码: 312-323
• 关键词: nonconcave penalized likelihood; proportional hazards model; variable selection; regression variables; oracle properties; Cross-validation; adaptive lasso; shrinkage; number; ORDER

摘要

We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators This approach relies heavily on the choice of regularization parameter, which controls the model complexity In this paper, we propose employing the generalized in criterion. encompassing the commonly used Akaike in criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter Our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches We show that the BIC-type selector enables identification of the true model consistently, and the resulting estimator possesses the oracle property in the terminology of Fan and Li (2001) In contrast, however, the AIC-type selector tends to overfit with positive probability We further show that the AIC-type selector is asymptotically loss efficient. while the BIC-type selector is not Our simulation results confirm these theoretical findings. and an empirical example is presented Some technical proofs are given in the online supplementary material