Sparse Minimum Discrepancy Approach to Sufficient Dimension Reduction with Simultaneous Variable Selection in Ultrahigh Dimension

• 成果类型: Article
• 署名作者: Qian, Wei; Ding, Shanshan; Cook, R. Dennis
• 署名单位: University of Delaware; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1497498
• 发表日期: 2019
• 页码: 1277-1290
• 关键词: sliced inverse regression; adaptive lasso; matrix; shrinkage

摘要

Sufficient dimension reduction (SDR) is known to be a powerful tool for achieving data reduction and data visualization in regression and classification problems. In this work, we study ultrahigh-dimensional SDR problems and propose solutions under a unified minimum discrepancy approach with regularization. When p grows exponentially with n, consistency results in both central subspace estimation and variable selection are established simultaneously for important SDR methods, including sliced inverse regression (SIR), principal fitted component (PFC), and sliced average variance estimation (SAVE). Special sparse structures of large predictor or error covariance are also considered for potentially better performance. In addition, the proposed approach is equipped with a new algorithm to efficiently solve the regularized objective functions and a new data-driven procedure to determine structural dimension and tuning parameters, without the need to invert a large covariance matrix. Simulations and a real data analysis are offered to demonstrate the promise of our proposal in ultrahigh-dimensional settings. Supplementary materials for this article are available online.