A Semiparametric View to Dimension Reduction: Estimation,

Inference and Efficiency

Yanyuan Ma

Department of Statistics

Texas A&M University

Engr 4201 (CS conference room)

4400 University Drive, Fairfax, VA 22030

Time: 3:00 P.M. - 4:00 P.M.

Date: Tuesday, Mar 18, 2014 



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. We further illustrate how to perform inference and derive efficient estimators with proper parameterization. Very different results are obtained in different common dimension reduction models.

Yunpeng Zhao, PhD

Assistant Professor
Department of Statistics
Volgenau School of Engineering
George Mason University
Engineering Building, Room 1719, MS 4A7
4400 University Drive
Fairfax, VA 22030-4444
Phone: 703-993-1674
Email: [log in to unmask]