Translator Disclaimer
June 2019 Sequential multiple testing with generalized error control: An asymptotic optimality theory
Yanglei Song, Georgios Fellouris
Ann. Statist. 47(3): 1776-1803 (June 2019). DOI: 10.1214/18-AOS1737

Abstract

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_{1}$ false positives and at least $k_{2}$ false negatives are simultaneously controlled. For each formulation, the optimal expected sample size is characterized, to a first-order asymptotic approximation as the error probabilities go to 0, and a novel multiple testing procedure is proposed and shown to be asymptotically efficient under every signal configuration. These results are established when the data streams for the various hypotheses are independent and each local log-likelihood ratio statistic satisfies a certain strong law of large numbers. In the special case of i.i.d. observations in each stream, the gains of the proposed sequential procedures over fixed-sample size schemes are quantified.

Citation

Download Citation

Yanglei Song. Georgios Fellouris. "Sequential multiple testing with generalized error control: An asymptotic optimality theory." Ann. Statist. 47 (3) 1776 - 1803, June 2019. https://doi.org/10.1214/18-AOS1737

Information

Received: 1 August 2016; Revised: 1 April 2018; Published: June 2019
First available in Project Euclid: 13 February 2019

zbMATH: 07053526
MathSciNet: MR3911130
Digital Object Identifier: 10.1214/18-AOS1737

Subjects:
Primary: 62L10

Rights: Copyright © 2019 Institute of Mathematical Statistics

JOURNAL ARTICLE
28 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 3 • June 2019
Back to Top