Stable Dimension Reduction

• Activity Number: 279
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Wenbo Wu*+ and Xiangrong Yin
• Companies: University of Georgia and University of Georgia
• Keywords: dimension reduction ; Grassmann manifold ; penalized method ; subsampling

Abstract

Many penalized dimension reduction methods provide estimation results with one or more tuning parameters involved. These results could be instable due to the sensitiveness to the tuning parameter values. We introduce stable estimation procedures in different aspects of dimension reduction. We first propose stable methods in estimating structural dimension which only selects the correct directions in central subspace with no false positive selection. We then propose a general Grassmann manifold estimation approach to give sparse estimation of basis directions of central subspace. For obtaining non-sparse estimation of basis directions of central subspace, we develop an ensemble methods based on sub-sampling. Theoretical supports are established and efficacy of proposed stable methods is demonstrated by real and simulated data.