A Perturbation Method for Inference on Adaptive LASSO Regression Estimates

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jessica Minnier*+ and Tianxi Cai
• Companies: Harvard University and Harvard School of Public Health
• Keywords: high-dimensional data ; variable selection ; regularized regression ; adaptive Lasso

Abstract

Analysis of massive "omics' data often seeks to identify a subset of important genes or proteins that are associated with disease outcomes. Robust regularization methods can simultaneously perform variable selection and estimation in such high-dimensional data settings. Adaptive LASSO, in particular, gives consistent and asymptotically normal estimates. However, in finite samples, it remains difficult to construct an estimate of the covariance matrix of the parameter estimates. We propose a perturbation method to approximate the distribution of the adaptive LASSO parameter estimates, which provides a simple way to estimate the covariance matrix and confidence regions. Through simulations we verify the ability of this method to give accurate inference and compare it to other standard methods. We illustrate our proposals with a study relating HIV drug resistance to genetic mutations.