One- and Two-Sided Composite-Composite Tests in Gaussian Mixture Models

• Activity Number: 368 - AOS Lecture
• Type: Invited
• Date/Time: Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
• Sponsor: IMS
• Author(s): Alexandra Carpentier* and Nicolas Verzelen and Etienne Roquain and Sylvain Delattre
• Companies: OvGU and INRAE and Universite Paris Descartes and Universite Paris Descartes
• Keywords: composite-composite tests; Gaussian mixtures; Sparse models

Abstract

We introduce one-sided versions of Huber’s contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation of the mean of uncorrupted samples (minimum effect) and selection of corrupted samples (outliers). This is also related to a problem of FDR control in multiple testing. In this talk, we will first discuss the case where both noise and contamination are Gaussian, and relate it to a specific composite-composite testing problem in Gaussian mixture model. We will then discuss the case of more general contaminations and see how the rates deteriorate slightly.

(based on joint works with Nicolas Verzelen, Etienne Roquain and Sylvain Delattre)