Confidence Sets Based on the Lasso Estimator

• Activity Number: 600
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Karl Ewald* and Ulrike Schneider
• Companies: Vienna University of Technology and Vienna University of Technology
• Keywords: LASSO ; model-selection ; linear regression model ; confidence sets

Abstract

In a linear regression model with fixed dimension, we investigate the distribution of the LASSO estimator in finite samples as well as in an asymptotic setup. In finite samples and asymptotically, in the case where the LASSO estimator is tuned to perform conservative model-selection, we derive formulas for computing the minimal coverage probability of the entire parameter vector for a large class of sets. This enables the construction of valid confidence sets based on the LASSO estimator. The choice of shape for the confidence sets is also discussed. Moreover, in the case where the LASSO estimator is tuned to enable consistent model-selection, we give a simple confidence set with minimal coverage probability converging to one. The findings are a generalization of results of Poetscher & Schneider (Electron. J. Stat., 2010).