On a Principal Varying Coefficient Model

• 成果类型: Article
• 署名作者: Jiang, Qian; Wang, Hansheng; Xia, Yingcun; Jiang, Guohua
• 署名单位: National University of Singapore; Peking University; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.736904
• 发表日期: 2013
• 页码: 228-236
• 关键词: dynamic-factor model; efficient estimation; spline estimation; inferences; regression

摘要

We propose a novel varying coefficient model (VCM), called principal varying coefficient model (PVCM), by characterizing the varying coefficients through linear combinations of a few principal functions. Compared with the conventional VCM, PVCM reduces the actual number of nonparametric functions and thus has better estimation efficiency. Compared with the semivarying coefficient model (SVCM), PVCM is more flexible but with the same estimation efficiency when the number of principal functions in PVCM and the number of varying coefficients in SVCM are the same. Model estimation and identification are investigated, and the better estimation efficiency is justified theoretically. Incorporating the estimation with the L-1 penalty, variables in the linear combinations can be selected automatically, and hence, the estimation efficiency can be further improved. Numerical experiments suggest that the model together with the estimation method is useful even when the number of covariates is large. Supplementary materials for this article are available online.