A Semiparametric Approach to Dimension Reduction.

نویسندگان

  • Yanyuan Ma
  • Liping Zhu
چکیده

We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction 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.

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عنوان ژورنال:
  • Journal of the American Statistical Association

دوره 107 497  شماره 

صفحات  -

تاریخ انتشار 2012