A CONSISTENT INDEPENDENCE TEST via PROJECTED MUTUAL INFORMATION

• Activity Number: 247 - Sufficient Dimension Reduction and High-Dimensional Data
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Zhanrui Cai* and Yaowu Zhang and Liping Zhu and Runze Li and Xu Guo
• Companies: Penn State University and Shanghai University of Finance and Economics and Renmin University of China and Penn State University and Beijing Normal University
• Keywords: Independence test; Local alternative; Mutual information; Semiparametric efficiency; Sufficient dimension reduction

Abstract

In this paper, we propose a nonparametric independence test based on the mutual information. Distinguished from the previous work, we propose to estimate the mutual information via a conditional density form, whose dimension could be reduced to 1 with novel projection methods. The optimal projection direction, which we name as maximum unit direction, is estimated by maximizing a penalized mutual information. An independence test is later on carried out based on the newly estimated mutual information and is shown to be insensitive to the dimensions. The test is consistent against all dependent alternatives, and could detect local alternatives at an exact rate. Numerical results indicate that the test is more powerful compared with other existing independence tests.