A Theoretical Note on Optimal Sufficient Dimension Reduction with Singularity

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Jae Keun Yoo*
• Companies: Ewha Womans University
• Keywords: chi-square test ; minimum discrepancy approach, ; singularity ; sufficient dimension reduction

Abstract

In this paper, we discuss an optimal sufficient dimension reduction through minimizing a quadratic objective function proposed by Cook and Ni (2005) with singular inner-product matrix. Within a less restrictive class of inner-product matrices, a generalized inverse of the consistent estimator of the asymptotic covariance matrix gives us the benefit of chi-square statistic and asymptotic efficiency within a subclass.