SOME THEORY ABOUT EFFICIENT DIMENSION REDUCTION REGARDING THE INTERACTION BETWEEN TWO RESPONSES

• 成果类型: Article
• 署名作者: Luo, Wei
• 署名单位: Zhejiang University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2463
• 发表日期: 2025
• 页码: 245-267
• 关键词: propensity score; regression

摘要

Efficient dimension reduction regarding the interaction between two response variables, which facilitates statistical analysis in multiple important application scenarios, was initially discussed by Luo (J. R. Stat. Soc. Ser. B. spaces were introduced, and, under mild conditions on the predictor, they were equated with the family of dual inverse regression subspaces. Besides the general framework, however, limited theory has been proposed to uncover the mystery of these spaces. In this paper, we propose a thorough characterization of the family of dual inverse regression subspaces, including their uniform lower and upper bounds, their explicit forms, their consistent and exhaustive estimation, some interesting special cases, and certain subfamilies that have desired sparsity. In addition, we extend some of these results to provide more insights into the efficient dimension reduction subspaces under the general settings, including their uniform lower and upper bounds, and the sufficient and necessary conditions for the uniqueness of the space that are assessable in practice. These results largely complete the theoretical foundation for the new type of dimension reduction, and, as such, enhance its applicability in statistical problems such as missing data analysis and causal inference. The latter is illustrated by simulation studies and a real data example at the end.