I will review the lasso method and show an example of its utility in cancer diagnosis via mass spectometry. Then I will consider the testing the significance of the terms in afitted regression, fit via the lasso. I will present a novel test statistic for this problem, and show that it has a simple asymptotic null distribution. This work builds on the least angle regression approach for fitting the lasso, and the notion of degrees of freedom for adaptive models (Efron 1986) and for the lasso (Efron et. al 2004, Zou et al 2007). We give examples of this procedure, discuss extensions to generalized linear models and the Cox model, and describe an R language package for its computation.
This work is joint with Richard Lockhart (Simon Fraser University), Jonathan Taylor (Stanford Univ), and Ryan Tibshirani (Carnegie Mellon University).