A1031
Title: Bootstrap inference for least angle regression
Authors: Daniel Nordman - Iowa State University (United States) [presenting]
Karl Gregory - University of South Carolina (United States)
Abstract: Least angle regression (LARS) is a well-known algorithm for variable selection in linear regression models, which provides an alternative to forward selection. However, little is known about the distributional behavior of LARS estimators, which hinders inference with LARS. The purpose is to overview some newly established distributional properties of LARS estimators, where the latter may be viewed as estimating variable importance correlations at the population level. These distributional results also provide a helpful perspective for understanding the mechanics of LARS. LARS estimators have large-sample distributional limits that may be either normal or non-normal, depending on whether estimators are capturing a true population signal or not. However, despite these complications, a bootstrap approach can be shown to validly approximate the distributional structure of LARS estimators, and, thereby, the bootstrap allows for useful inference in LARS regarding variable importance. The bootstrap method and results are illustrated in numerical studies and examples.
