Bayesian Statistics Seminar
North Carolina State University
presents
Dr. Lexin Li
North Carolina State University
"Regularized Sufficient Dimension Reduction and Variable Selection"
ABSTRACT
Sufficient dimension reduction (SDR) has proven effective to transform high dimensional problems to low dimensional projections, while losing no regression information and pre-specifying no parametric model during the phase of dimension reduction. However, existing SDR methods suffer from the fact that each dimension reduction component is a linear combination of all the original predictors, so that it is difficult to interpret the resulting estimates. We first present a unified estimation strategy, which combines a regression-type formulation of SDR methods with shrinkage estimation, to produce both sparse and accurate solutions. We next propose a regularized estimation strategy, which is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimator achieves consistency in variable selection without requiring any traditional model, meanwhile retaining root-n estimation consistency of the dimension reduction basis. Both simulation studies and real data analyses are reported.
Slides of the talk available.
Wednesday, March, 21, 2007
4:00 - 5:00 pm
208 Patterson Hall