*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**:**0**0 **P**.M. - **4**:**0**0 **P**.M.*

*Date: **Tuesday**, **Mar 18**, 201**4*


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

Yunpeng Zhao, PhD

Assistant Professor
Department of Statistics
Volgenau School of Engineering <[log in to unmask]>
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]