Efficient estimation in sufficient dimension reduction

Yanyuan Ma, Liping Zhu

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)250-268
Number of pages19
JournalAnnals of Statistics
Issue number1
StatePublished - Feb 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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