Higher-Order Properties of the Bootstrap in High-Dimensional Problems

• Activity Number: 287
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: ASA
• Author(s): Soumendra N. Lahiri*+ and Arindam Chatterjee
• Companies: North Carolina State University and Indian Statistical Institute
• Keywords: ALASSO ; Oracle distribution ; Penalized regression ; Regularization ; Second order correctness

Abstract

This talk considers post variable selection inference in high dimensional penalized regression problems. Exact rate of apprximation by the oracle limit law is determined. It is shown that this can lead to a very poor finite sample performance, which can be typically improved by applying the bootstrap. It is also shown that the bootstrap applied to a specially constructed bias-corrected studentized pivot is second order correct. Further, the level of accuracy attained by the bootstrap in this high dimensional problem is comparable to the best possible rate in the traditional linear regression set up with a fixed and finite number of covariates.