Open Access
October 2018 Global testing against sparse alternatives under Ising models
Rajarshi Mukherjee, Sumit Mukherjee, Ming Yuan
Ann. Statist. 46(5): 2062-2093 (October 2018). DOI: 10.1214/17-AOS1612


In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illustrated under the Curie–Weiss model where we observe the effect of a “thermodynamic” phase transition. In particular, the critical state exhibits a subtle “blessing of dependence” phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop a testing procedure that is broadly applicable to account for dependence and show that it is asymptotically minimax optimal under fairly general regularity conditions.


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Rajarshi Mukherjee. Sumit Mukherjee. Ming Yuan. "Global testing against sparse alternatives under Ising models." Ann. Statist. 46 (5) 2062 - 2093, October 2018.


Received: 1 November 2016; Revised: 1 May 2017; Published: October 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06964326
MathSciNet: MR3845011
Digital Object Identifier: 10.1214/17-AOS1612

Primary: 62C20 , 62G10 , 62G20

Keywords: Detection boundary , Ising models , Phase transitions , sparse signals

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 5 • October 2018
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