Sparse Sliced Inverse Regression via Lasso

• 成果类型: Article
• 署名作者: Lin, Qian; Zhao, Zhigen; Liu, Jun S.
• 署名单位: Tsinghua University; Tsinghua University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; Harvard University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1520115
• 发表日期: 2019
• 页码: 1726-1739
• 关键词: VARIABLE SELECTION; Dimension Reduction; index models; Consistency; shrinkage; PURSUIT

摘要

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieves the optimal convergence rate under certain sparsity conditions when p is of order , where lambda is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples. for this article are available online.