Computing and Mathematical Sciences Colloquium

  In this talk I propose new inference tools for least angle and forward stepwise regression.   I first present a general scheme for valid inference after any selection event that can be described as the observation vector y falling into a polyhedron.   Following this, I derive a new procedure called the "spacing test" which provides exact conditional tests at any step of the least angle regression (LAR) algorithm,   as well as "selection intervals" for the appropriate underlying regression parameters. Remarkably, these tests and intervals account correctly for the adaptive selection performed by LAR.   I will apply the same framework to yield selection-adjusted tests and intervals for forward stepwise regression in linear models, generalized linear models and other settings such as the Cox model.   Finally I will briefly discuss current work extending these ideas to the PCA setting. Joint work with Jonathan Taylor, Richard Lockhart and Ryan J. Tibshirani.