Theory and applications of finite mixture models

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Heterogeneity in the data is the norm, while homogeneity is the exception. Mixture models provide flexible means of handling heterogeneity in data. However, statistical inference for mixture models is particularly challenging due to the irregularity of the problem from a classical parametric likelihood inference point of view. Therefore, mixture models are often viewed as one of the most important classes of non-regular statistical models. The long-term goal of this research program is to develop innovative methodologies in the fields of mixture models, empirical likelihood and their interface, and to use such methodologies in solving statistical problems in a variety of applications for which no simple solutions exist. This proposal is composed of three parts. The short term objectives are as follows: 1) to develop theory and methodology for semiparametric functional mixture regression models; 2) to explore the use of mixture models in circular data analysis; 3) to explore the use of empirical likelihood methods in multivariate mixture models. This research program is novel and multi-faceted. It will draw on several important statistical tools such as mixture models, functional data analysis, empirical likelihood methods to tackle important scientific questions. It raises several theoretical problems of interest, and in addition, success of this research program will yield significant contribution to the theory and applications of mixture models. In turn, these results will be useful in problems arising in many fields in the natural sciences and engineering. The theory and methodologies developed will also have great scope for extensions and applications.