Rejoinder to “A Significance Test for the Lasso”

Abstract

We would like to thank the editors and referees for their considerable efforts that improved our paper, and all of the discussants for their feedback, and their thoughtful and stimulating comments. Linear models are central in applied statistics, and inference for adaptive linear modeling is an important active area of research. Our paper is clearly not the last word on the subject! Several of the discussants introduce novel proposals for this problem; in fact, many of the discussions are interesting “mini-papers ” on their own, and we will not attempt to reply to all of the points that they raise. Our hope is that our paper and the excellent accompanying discussions will serve as a helpful resource for researchers interested in this topic. Since the writing of our original paper, we have (with many our of graduate students) extended the work considerably. Before responding to the discussants, we will first summarize this new work because it will be relevant to our responses. • As mentioned in the last section of the paper, we have derived a “spacing ” test of the global null hypothesis, β ∗ = 0, which takes the for