EFFICIENT ESTIMATION IN SUFFICIENT 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; Shanghai University of Finance & Economics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1072
• 发表日期: 2013
• 页码: 250-268
• 关键词: sliced inverse regression; semiparametric estimators; models

摘要

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions. Our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods.