Exact Inference for Linear and Logistic Regression After Model Selection

• Activity Number: 80
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jason Lee*+ and Jonathan Taylor and Yuekai Sun and Dennis Sun
• Companies: Stanford University and Stanford University and Stanford University and Stanford University
• Keywords: Post model selection inference ; confidence intervals ; lasso ; marginal screening ; correlation screening

Abstract

We develop a framework for inference in Linear regression and Logistic regression after model selection using marginal screening or Lasso. At the core of this framework is a result that characterizes the exact (non-asymptotic) distribution of a pivot.

This pivot allows us to (i) construct valid confidence intervals for the selected coefficients that account for the selection procedure, and (ii) devise a test statistic that has an exact (non-asymptotic) $\unif(0,1)$ distribution under the null hypothesis that all relevant variables have been included in the model.

We will also discuss extensions of the methodology to other GLM regression.