Efficiency loss and the linearity condition in dimension reduction

• 成果类型: Article
• 署名作者: Ma, Yanyuan; Zhu, Liping
• 署名单位: Texas A&M University System; Texas A&M University College Station; Shanghai University of Finance & Economics
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass075
• 发表日期: 2013
• 页码: 371383
• 关键词: regression; parameters

摘要

Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation.