Estimation for Conditional Independence Multivariate Finite Mixture Models

The conditional independence assumption for nonparametric multivariate finite mixture models may be considered to be a weaker form of the well-known conditional independence assumption for random effects models for longitudinal data. After summarizing important recent identifiability results, this article describes and extends an algorithm for estimation of the parameters in these models. The algorithm works for any number of components and any dimensionality of at least three, and it possesses a descent property and can be easily adapted to situations where the data is grouped in blocks of conditionally independent variables. We discuss how to adapt this algorithm to various locationscale models that link component densities, and we even adapt it to a particular class of univariate mixture problems in which the components are assumed symmetric. We also give an example of possible bandwidth selection procedure for our algorithm. The effectiveness of the new algorithm is demonstrated in a simulation study and two psychometric datasets. ∗Laboratoire MAPMO, Université d’Orléans & CNRS UMR 6628, France, [email protected] †Department of Statistics, Pennsylvania State University, University Park PA 16801, USA, [email protected] ‡Department of Statistics, Purdue University, West Lafayette, IN 47907, USA, [email protected]