A0594
Title: Statistical inference for normal mixtures with unknown number of components
Authors: Mian Huang - Shanghai University of Finance and Economics (China) [presenting]
Abstract: Statistical inference for normal mixture models with an unknown number of components has long been challenging due to non-identifiability, degenerated Fisher matrix, and boundary parameters. A penalized likelihood estimation procedure is proposed for mixtures of normals with an unknown number of components to achieve both the order selection consistency and the local root-n convergence rate for the component parameters estimators. We show that the proposed new estimator could avoid being trapped in certain degenerated regions of the non-identifiable subset of the parameter space for over-fitted normal mixture models so that a regular asymptotic quadratic Taylor expansion of the mixture log-likelihood could be derived. With a suitable penalty function on mixing proportions, the new estimator is consistent on the order selection and has an asymptotic normal distribution. Our derived sparsity conditions also reveal some surprising but interesting differences among some commonly used penalty functions and explain why the performance of some popularly used penalty functions, such as Lasso and SCAD, provide unsatisfactory results in the order selection of the mixture model.
