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*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* *Abstract* 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 <[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]