A Semiparametric View to Dimension Reduction: Estimation,
Inference and Efficiency
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.