SEMI-PARAMETRIC INFERENCE IN A BIVARIATE (MULTIVARIATE) MIXTURE MODEL
Denis H. Y. Leung, Jing Qin · Singapore Management University Institutional Knowledge (InK) (Singapore Management University) · 2006
We consider estimation in a bivariate mixture model in which the com- ponent distributions can be decomposed into identical distributions. Previous ap- proaches to estimation involve parametrizing the distributions. In this paper, we use a semi-parametric approach. The method is based on the exponential tilt model of Anderson (1979), where the log ratio of probability (density) functions from the bivariate components is linear in the observations. The proposed model does not re- quire training samples, i.e., data with conrmed component membership. We show that in bivariate mixture models, parameters are identiable. This is in contrast to previous works, where parameters are identiable if and only if each univariate marginal model is identiable (Teicher (1967)).