A semiparametric approach to canonical analysis

• 成果类型: Article
• 署名作者: Xia, Yingcun
• 署名单位: National University of Singapore
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2007.00647.x
• 发表日期: 2008
• 页码: 519-543
• 关键词: dimension reduction; MULTIPLE-REGRESSION; models

摘要

Classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables. We propose a method, called semiparametric canonical analysis, to generalize canonical correlation analysis to incorporate the important non-linear association. Semiparametric canonical analysis is easy to implement and interpret. Statistical properties are proved. A consistent estimation method is developed. Selection of significant semiparametric canonical analysis components is discussed. Simulations suggest that the methods proposed have satisfactory performance in finite samples. One environmental data set and one data set in social science are investigated, in which non-linear canonical associations are observed and interpreted.