New Theoretical Grounding of Nonparametric Estimation for Conditional Independence Multivariate Finite Mixture Models

For the nonparametric estimation of multivariate finite mixture models with the conditional independence assumption, we propose a new formulation of the objective function in terms of penalized smoothed Kullback-Leibler distance. The nonlinear majorization-minimization smoothing algorithm (NMMS) is derived from this perspective. A more precise monotonicity property of the algorithm is discovered and the existence of a solution to the main optimization problem is proved for the first time.