Asset Details
Do you wish to reserve the book?
POST HOC CONFIDENCE BOUNDS ON FALSE POSITIVES USING REFERENCE FAMILIES
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
POST HOC CONFIDENCE BOUNDS ON FALSE POSITIVES USING REFERENCE FAMILIES
Do you wish to request the book?
POST HOC CONFIDENCE BOUNDS ON FALSE POSITIVES USING REFERENCE FAMILIES
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
POST HOC CONFIDENCE BOUNDS ON FALSE POSITIVES USING REFERENCE FAMILIES
2020
Overview
We follow a post hoc, “user-agnostic” approach to false discovery control in a large-scale multiple testing framework, as introduced by Genovese and Wasserman [J. Amer. Statist. Assoc. 101 (2006) 1408–1417], Goeman and Solari [Statist. Sci. 26 (2011) 584–597]: the statistical guarantee on the number of correct rejections must hold for any set of candidate items, possibly selected by the user after having seen the data. To this end, we introduce a novel point of view based on a family of reference rejection sets and a suitable criterion, namely the joint familywise error rate over that family (JER for short). First, we establish how to derive post hoc bounds from a given JER control and analyze some general properties of this approach. We then develop procedures for controlling the JER in the case where reference regions are p-value level sets. These procedures adapt to dependencies and to the unknown quantity of signal (via a step-down principle). We also show interesting connections to confidence envelopes of Meinshausen [Scand. J. Stat. 33 (2006) 227–237]; Genovese and Wasserman [J. Amer. Statist. Assoc. 101 (2006) 1408–1417], the closed testing based approach of Goeman and Solari [Statist. Sci. 26 (2011) 584–597] and to the higher criticism of Donoho and Jin [Ann. Statist. 32 (2004) 962–994]. Our theoretical statements are supported by numerical experiments.
Publisher
Institute of Mathematical Statistics
Subject
