Forward Variable Selection for Sparse Ultra-High-Dimensional Varying Coefficient Models

• Activity Number: 625
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Ming-Yen Cheng* and Toshio Honda and Jin-Ting Zhang
• Companies: National Taiwan University and Hitotsubashi University and National University of Singapore
• Keywords: B-spline ; EBIC ; independence screening ; marginal model ; sub-Gaussion error ; structure identification

Abstract

Varying coefficient models have numerous applications in a wide scope of scientific areas. On the other hand, in the new era of big data, it is challenging to select the relevant variables when there are a large number of candidate ones. Recently several work are focused on coping with this important problem based on sparsity assumptions; they are subject to some limitations, however. We introduce an appealing variable selection procedure and discuss in detail its advantages over existing methods. The proposed method selects important variables sequentially according to a sum of squares criterion, and it employs an EBIC- or BIC-based stopping rule. Clearly, it is simple to implement and fast to compute. Furthermore, it possesses many other desirable properties from both theoretical and numerical viewpoints. We establish rigorous selection consistency results when either EBIC or BIC is used as the stopping criterion, under sub-Gaussian errors and some mild regularity conditions. Notably, unlike existing methods, an extra screening step is not required to ensure selection consistency. Simulation and empirical studies are used to show the efficacy and usefulness of our procedure.