Detecting of sparse and weak effects in high dimensions

Tatjana Pavlenko

 In this talk, we show how goodness-of-fit test statistics based on sup-functionals  of weighted empirical processes can be effectively applied to various  problems of signal detection and classification in high-dimensional,  sparse models.  The weight functions employed are Erdős-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian bridge.
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 joint work with Natalia Stepanova, Carleton University, Canada.