Tatjana Pavlenko: Large-scale statistical inference: detecting sparse and weak effects

Tid: On 2018-12-12 kl 15.15 - 16.15

Föreläsare: Tatjana Pavlenko (KTH)

Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Abstract: In this talk, we introduce a unified family of goodness-of-fit test statistics based on sup-functionals of weighted empirical processes and show that these statistics can be effectively applied to various subtle problems of signal detection and feature selection in high-dimensional, sparse models. The weight functions employed are Erdős-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian bridge. We show that the proposed test statistics achieve the optimal detection boundary and, when distinguishing between the null and alternative hypotheses, perform optimally adaptively to unknown sparsity and size of the non-null effects. The obtained results demonstrate the advantage of our approach to the problems of signal detection and classification in sparse models over a common approach that utilizes regularly varying weight functions.  

(This is a joint work with Natalia Stepanova, Carleton University, Canada.)