Applications of Model-Averaging for High Dimensional Inference

Abstract

This dissertation builds up to and develops Model-Averaged Inferential Learning (MAIL), a generally useful method of inference for linear regression problems when $p >> n$. The first chapter adds to the literature on using model averaging for variable selection diagnostics. The second chapter compares inferential results from post-selection methods to un-adjusted methods from the best data-driven model. The third chapter proposes and demonstrates the theoretical and practical value of MAIL. MAIL is shown to give valid confidence intervals for the full linear targets of selected variables across a wide range of challenging simulation settings.