Online Program Home
My Program

Abstract Details

Activity Number: 108 - Multivariate Extremes: Theory and Applications
Type: Invited
Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Risk Analysis
Abstract #300187 Presentation
Title: Multiple Testing and Extremes: Exact Signal Support Recovery in High Dimensions
Author(s): Zheng Gao and Stilian Stoev*
Companies: University of Michigan and University of Michigan
Keywords: relative stability; concentration of maxima; support recovery; strong classification boundary; thresholding estimators; Ramsey coloring theorem

We study the estimation of the support (set of non-zero components) of a high-dimensional signal observed with additive and dependent noise. With the usual parameterization of the size of the support set and the signal magnitude, we characterize a phase-transition phenomenon akin to the Ingster’s signal detection boundary. We show that when the signal is above the so-called strong classification boundary, thresholding estimators achieve asymptotically perfect support recovery. This is so under arbitrary error dependence assumptions, provided that the marginal error distribution has rapidly varying tails. Conversely, under mild dependence conditions on the noise, we show that no thresholding estimators can achieve perfect support recovery if the signal is below the boundary. For log-concave error densities, the thresholding estimators are shown to be optimal and hence the strong classification boundary is universal, in this setting.

The proofs exploit a concentration of maxima phenomenon, known as relative stability. We obtain a complete characterization of the relative stability phenomenon for dependent Gaussian noise via Slepian, Sudakov-Fernique bounds and Ramsey theory.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2019 program