Sliced regression for dimension reduction

• 成果类型: Article
• 署名作者: Wang, Hansheng; Xia, Yingcun
• 署名单位: Peking University; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214508000000418
• 发表日期: 2008
• 页码: 811-821
• 关键词: principal hessian directions; inverse regression; central subspace; Visualization; estimators

摘要

A new dimension-reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed. Compared with the traditional inverse regression methods [e.g., sliced inverse regression (SIR)], the new method is free of the linearity condition and has much better estimation accuracy. Compared with the direct estimation methods (e.g., MAVE), the new method is much more robust against extreme values and can capture the entire central subspace (CS) exhaustively. To determine the CS dimension, a consistent cross-validation criterion is developed. Extensive numerical studies, including a real example, confirm our theoretical findings.