One and two sided composite-composite tests in Gaussian mixture models

Abstract: Finding an efficient test for a testing problem is often linked to the problem of estimating a given function of the data. When this function is not smooth, it is necessary to approximate it cleverly in order to build good tests.
In this talk, we will discuss two specific testing problems in Gaussian mixtures models. In both, the aim is to test the proportion of null means. The aforementioned link between sharp approximation rates of non-smooth objects and minimax testing rates is particularly well illustrated by these problems.

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

Biography: Alexandra Carpenter is since October 2017 chair of Mathematical Statistics and Machine Learning in the Institut für Mathematische Stochastik (IMST), Fakultät für Mathematik (FMA), in the Otto-von-Guericke-Universität Magdeburg. Prior to that, she was between 2015 and 2017 the group leader of the DFG Emmy Noether group MuSyAD on theoretical anomaly detection in the Universitaet Potsdam, and between 2012 and 2015 in the StatsLab in the University of Cambridge as a research associate, working with Richard Nickl. She finished her PhD in 2012 in INRIA Lille Nord-Europe under the supervision of Remi Munos and on the topic of bandit theory. Her research interests are in machine learning and mathematical statistics with an emphasis on composite testing problems, adaptive inference in high and infinite dimension and sequential learning (e.g. bandit theory).