On the Optimality of Sliced Inverse Regression in High Dimensions

• Activity Number: 321
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Qian Lin* and Xinran Li and Jun S. Liu
• Companies: Harvard and Harvard and Harvard
• Keywords: Sufficient Dimension Reducation ; sliced inverse regression ; Minimax Rate ; sparsity

Abstract

The optimal rate of estimating the sufficient dimension reduction in high dimension is an intrigue problem. In this paper, we proved that, over a large class of functions, the sliced inverse regression is optimal for single index models. We also provide the best known upper bound of the convergence rate for multiple index models.