科研成果详情

Finite mixture models (FMM) have received increasing attention in recent years and have proven to be useful in modeling heterogeneous data with a finite number of unobserved sub-population. FMM are a powerful and flexible tool for modeling complex data. In this article, we study the asymptotic distribution of the appropriately linear normalized coordinatewise maximum and minimum under multivariate FMM from independent, but not obligatory identically distributed random vectors. We obtain sufficient conditions for this weak convergence, as well as the limit forms. Sufficient conditions for this convergence when the components of the mixture have different linear normalization have been derived. Illustrative examples are provided, which lend further support to our theoretical results.