Open Access
February 2013 Efficient estimation in sufficient dimension reduction
Yanyuan Ma, Liping Zhu
Ann. Statist. 41(1): 250-268 (February 2013). DOI: 10.1214/12-AOS1072


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.


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Yanyuan Ma. Liping Zhu. "Efficient estimation in sufficient dimension reduction." Ann. Statist. 41 (1) 250 - 268, February 2013.


Published: February 2013
First available in Project Euclid: 26 March 2013

zbMATH: 1347.62089
MathSciNet: MR3059417
Digital Object Identifier: 10.1214/12-AOS1072

Primary: 62H12 , 62J02
Secondary: 62F12

Keywords: central subspace , Dimension reduction , estimating equations , Semiparametric efficiency , sliced inverse regression

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 1 • February 2013
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