The Annals of Statistics
- Ann. Statist.
- Volume 46, Number 5 (2018), 2062-2093.
Global testing against sparse alternatives under Ising models
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.
Ann. Statist., Volume 46, Number 5 (2018), 2062-2093.
Received: November 2016
Revised: May 2017
First available in Project Euclid: 17 August 2018
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Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming. Global testing against sparse alternatives under Ising models. Ann. Statist. 46 (2018), no. 5, 2062--2093. doi:10.1214/17-AOS1612. https://projecteuclid.org/euclid.aos/1534492829
- Supplement to “Global testing against sparse alternatives under Ising models”. The supplementary material contain the proofs of additional technical results.