SPARSE SIR: OPTIMAL RATES AND ADAPTIVE ESTIMATION

• 成果类型: Article
• 署名作者: Tan, Kai; Shi, Lei; Yu, Zhou
• 署名单位: East China Normal University; Fudan University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1791
• 发表日期: 2020
• 页码: 64-85
• 关键词: sliced inverse regression; Dimension Reduction; canonical correlation; central subspace; Consistency

摘要

Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.