Tensor Sliced Inverse Regression and Its Asymptotics

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Shanshan Ding*+ and Dennis Cook
• Companies: University of Minnesota and University of Minnesota
• Keywords: Tensor ; Sliced inverse regression ; sufficient dimension reduction ; central subspace ; central dimension folding subspace

Abstract

Sliced inverse regression (SIR) is a widely used non-parametric method for supervised dimension reduction. Conventional SIR mainly tackles simple data structure but is inappropriate for data with tensor-valued predictors. In this paper, we propose a new approach to extend SIR to this more general data structure and refer to it as tensor SIR. The proposed method can improve estimation accuracy and reduce computation cost in comparison to existing methods, such as dimension folding SIR. We in addition investigate its asymptotic properties and demonstrate its advantages by simulation and real data studies.