DMS Statistics and Data Science Seminar

Speaker: Lei Li, FDA

Title: Robust Divergence Based Inference for Finite Mixture Models

Abstract: Finite mixture models arise in several contemporary applications spanning various scientific disciplines. Existing algorithms for computing the estimates of parameters in such models include (i) EM algorithm, (ii) HMIX algorithm, and (iii) proximal point algorithm. It is well-known that estimators obtained from an application of the EM algorithm are not robust. In this presentation, we propose a new algorithm, called the DivMin algorithm, which include as a special case the EM algorithm, HMIX algorithm, and other proximal point algorithms. We investigate the population version and the sample version of the algorithm and establish various theoretical properties. Furthermore, when the divergence belongs to a subclass used in robust estimation, we show that the estimates are robust. We illustrate our results through several simulation studies and real data examples with and without regression settings.