Open AccessEFFICIENT ESTIMATION IN SUFFICIENT DIMENSION REDUCTION.
Author(s) -
Yanyuan Ma,
Liping Zhu
Publication year - 2013
Publication title -
pubmed
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.877
H-Index - 178
pISSN - 0090-5364
DOI - 10.1214/12-aos1072supp
Subject(s) - subspace topology , estimator , mathematics , dimension (graph theory) , inference , dimensionality reduction , mathematical optimization , reduction (mathematics) , sufficient dimension reduction , semiparametric model , algorithm , statistics , computer science , artificial intelligence , mathematical analysis , geometry , pure mathematics
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.