On Localized Dimension Reduction and Variable Selection

• Activity Number: 138
• Type: Invited
• Date/Time: Monday, August 3, 2009 : 10:30 AM to 12:20 PM
• Sponsor: ASA Special Interest Group on Statistical Learning and Data Mining
• Author(s): Xiangrong Yin*+ and Qin Wang and Bing Li and Zhihui Tang
• Companies: The University of Georgia and The University of Georgia and Penn State University and Penn State University
• Keywords: Central Subspace ; k-nearest-neighbor ; Sliced Inverse Sliced Inverse Regression

Abstract

We propose a novel approach to dimension reduction and variable selection based on localization. The method, to be called k-Nearest-Neighbor Sliced Inverse Regression (KNN-SIR), is developed to relax the restrictive linearity condition on the predictor, and to achieve exhaustive estimation of the dimension reduction space. Together with this estimator, we also introduce a testing procedure to estimate dimensionality, and a variable selection procedure to handle sparsity in the predictors. Finally, a fast algorithm of KNN-SIR is developed, which is especially useful huge data sets. We demonstrate the efficacy of our method by simulation and on real applications.