On Testing Common Indices for Two Multi-Index Models

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xuejing Liu*+ and Zhou Yu and Xuerong Meggie Wen and Robert Paige
• Companies: and University of Wisconsin and Department of Mathematics and Statistics, Missouri University of Science and Technology and Department of Mathematics and Statistics, Missouri University of Science and Technology
• Keywords: Multi-index model ; Sufficient dimension reduction ; Sliced inverse regression ; Central subspace

Abstract

We propose a link-free test for two multi-index models with identical indices via the sufficient dimension reduction (Li 1991; Cook 1998) approach. Test statistics are developed based upon three different sufficient dimension reduction methods: (i) sliced inverse regression, (ii) sliced average variance estimation and (iii) directional regression. The asymptotic null distributions of our test statistics are also derived. Monte Carlo studies are performed to investigate the efficacy of our proposed methods. A real-world application is also considered.