Shrinkage Estimation of the Varying Coefficient Model

• 成果类型: Article
• 署名作者: Wang, Hansheng; Xia, Yingcun
• 署名单位: Peking University; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.0138
• 发表日期: 2009
• 页码: 747-757
• 关键词: nonconcave penalized likelihood; variable selection; adaptive lasso; regression; inferences

摘要

The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator (LASSO). The new method can do nonparametric estimation and variable selection simultaneously. With a local constant estimator and the adaptive LASSO penalty the new method can identify the true model consistently, and that the resulting estimator can be as efficient as the oracle estimator Numerical studies clearly confirm our theories. Extension to other shrinkage methods(e.g. the SCAD. i.e., the Smoothly Clipped Absolute Deviation.) mid other smoothing methods is stiaightforward.