Penalized composite quasi-likelihood for ultrahigh dimensional variable selection

• 成果类型: Article
• 署名作者: Bradic, Jelena; Fan, Jianqing; Wang, Weiwei
• 署名单位: Princeton University; University of Texas System; University of Texas Health Science Center Houston
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2010.00764.x
• 发表日期: 2011
• 页码: 325-349
• 关键词: p-regression parameters; asymptotic-behavior; diverging number; M-ESTIMATORS; Lasso; p2/n

摘要

In high dimensional model selection problems, penalized least square approaches have been extensively used. The paper addresses the question of both robustness and efficiency of penalized model selection methods and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L-1-penalty. It is completely data adaptive and does not require prior knowledge of the error distribution. The weighted L-1-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias that is caused by the L-1-penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the method proposed that has both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L-1-L-2, and an optimal composite quantile method and evaluate their performance in both simulated and real data examples.