3261769be720b0fefbfffec05e9d9202-AuthorFeedback.pdf

We thank all reviewers for very helpful comments. This letter addresses the major questions raised by the reviewers. Please see the response below for "distribution assumptions" and "global null and We will correct our references and typos in the table. We shall elaborate more in our revised version to make these more clear. To conquer this issue, we provided high-probability guarantees in Section 2 and 3. Please also see Please see below for "global null and group of coefficients" and "more discussions We will elaborate more in our revised version when the eigen-spetra are not as nicely behaved.