Dimension Reduction for Multivariate Responses by Projection Onto Empirical Directions

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Armine Bagyan*+ and Arkady Tempelman and Bing Li
• Companies: Penn State University and Penn State University and Penn State University
• Keywords: dimension reduction ; multivariate response ; projections of the response

Abstract

We introduce a new method for sufficient dimension reduction with multivariate responses. This is inspired by an earlier work of Li, Wen and Zhu (2008), which reduces the multivariate response vector to a response random variable by projecting the former onto randomly sampled direction. In this work we propose to project the multivariate response vector onto the set of empirical directions (Li and Wang, 2007) rather than random directions. An advantage of this modification is that, unlike resampling, repeated applications of this method always yield numerically identical result. We develop the population-level properties of this method, such as unbiasedness, as well as its asymptotic properties, such as its square root n consistency and asymptotic normality. We also compare it with other sufficient dimension reduction methods for multivariate responses, such as projective resampling, and investigate its performance in several applied settings.