Inference on Non-nested and Mis-specified Finite Mixture Model selection

The first goal of this article is estimate a some finite mixture model when the data generating model is unknown and the competing models are mis-specified and non-nested. We have illustrated conditions under which we can estimate the underlying parameters. We discuss the formulation and theoretical results for this scope when the parameter space is identified. Finally, we turn to our main subject which is non-nested model selection test for this family of distributions. The simulation study confirms our theoretical results.