Envelopes and reduced-rank regression

• 成果类型: Article
• 署名作者: Cook, R. Dennis; Forzani, Liliana; Zhang, Xin
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; National University of the Littoral; State University System of Florida; Florida State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv001
• 发表日期: 2015
• 页码: 439456
• 关键词: Asymptotic Theory; estimator

摘要

We incorporate the nascent idea of envelopes (Cook et al., Statist. Sinica 20, 927-1010) into reduced-rank regression by proposing a reduced-rank envelope model, which is a hybrid of reduced-rank and envelope regressions. The proposed model has total number of parameters no more than either of reduced-rank regression or envelope regression. The resulting estimator is at least as efficient as both existing estimators. The methodology of this paper can be adapted to other envelope models, such as partial envelopes (Su & Cook, Biometrika 98, 133-46) and envelopes in predictor space (Cook et al., J. R. Statist. Soc. B 75, 851-77).