Speaker: Tudor Manole

Abstract: Three challenges which attract a great deal of attention in the current mixture model literature include (1) understanding the behaviour of parameter estimation in mixtures with a misspecified number of components, (2) estimating the number of components of a mixture, and (3) constructing estimators which are robust to misspecification of the component density functions. I will start by discussing some recent results regarding (1), to motivate a new method of Ho, Nguyen and Ritov which addresses (2) and (3). In the first part of the talk, the focus will be on a recent line of work by the first two authors, which characterizes the complicated behaviour of optimal rates of convergence for various classes of mixing measures. For instance, I will explain why the results of this theory warn against the use of maximum likelihood estimation for Gaussian mixture models with an incorrect number of components. In the second part of the talk, I will present the authors' proposed estimator of mixing measures, inspired by minimum Hellinger distance estimation. I will discuss its robustness properties, and show that it satisfies similar asymptotic properties as comparable likelihood-based approaches, under weaker assumptions.

The main paper is: https://arxiv.org/pdf/1709.08094.pdf The first part of the talk will mainly be based on the following two papers: http://www-personal.umich.edu/~minhnhat/AoS_2016.pdf and http://www-personal.umich.edu/~minhnhat/Ejs_2016.pdf