Dimension reduction for non-elliptically distributed predictors: second-order methods

• 成果类型: Article
• 署名作者: Dong, Yuexiao; Li, Bing
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq016
• 发表日期: 2010
• 页码: 279294
• 关键词: principal hessian directions; regression; extraction; moment

摘要

Many classical dimension reduction methods, especially those based on inverse conditional moments, require the predictors to have elliptical distributions, or at least to satisfy a linearity condition. Such conditions, however, are too strong for some applications. Li and Dong (2009) introduced the notion of the central solution space and used it to modify first-order methods, such as sliced inverse regression, so that they no longer rely on these conditions. In this paper we generalize this idea to second-order methods, such as sliced average variance estimation and directional regression. In doing so we demonstrate that the central solution space is a versatile framework: we can use it to modify essentially all inverse conditional moment-based methods to relax the distributional assumption on the predictors. Simulation studies and an application show a substantial improvement of the modified methods over their classical counterparts.