A semiparametric approach to dimension reduction

Yanyuan Ma, Liping Zhu

Research output: Contribution to journalArticle

80 Scopus citations

Abstract

We provide a novel and completely different approach to dimension-reduction problems from the existing literature.We cast the dimensionreduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension reduction techniques as special cases in this class. The semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact, the common assumption of linearity and/or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression. The semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example. This article has online supplementary material.

Original languageEnglish (US)
Pages (from-to)168-179
Number of pages12
JournalJournal of the American Statistical Association
Volume107
Issue number497
DOIs
StatePublished - Jul 2 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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