Bootstrap Inference for High-Dimensional Data

• Activity Number: 361
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Guoqing Diao*+ and Anand Vidyashankar
• Companies: George Mason University and George Mason University
• Keywords: Bootstrap inference ; Confidence region ; High-dimensional problem ; Hotelling's statistic ; Rademacher Chaos ; Random projection

Abstract

Inference for high-dimensional problems when the number of features exceed the sample size is challenging since the classical procedures based on Hotelling's statistic and their variants are not applicable due to the singularity of the sample covariance matrix. Recent attempts at addressing this issue using Gaussian random projections has not met with much success especially in the ultra high-dimensional problems. In this presentation, we describe an alternative approach based on an embedding into an infinite-dimensional space and alternate metrics to construct a test statistic. We describe a joint confidence region for the mean parameter vector and the use of Rademacher Chaos for bootstrap inference. Furthermore, we establish the theoretical validity of the bootstrap. Simulation studies and real-data examples are used to illustrate the methodology.