Comments on: High-dimensional simultaneous inference with the bootstrap

The authors should be congratulated on their insightful article proposing forms of residual and paired bootstrap methodologies in the context of simultaneous testing in sparse and high-dimensional linear models. We appreciate the clear exposition of their work, and the effectiveness of the proposed method. The authors advocate for the bootstrap of a complete high-dimensional estimate rather than the linearized part of the test statistic. We appreciate the opportunity to comment on several aspects of this article.