Theoretical grounding for estimation in conditional independence multivariate finite mixture models

ABSTRACT

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 penalised smoothed Kullback–Leibler distance. The nonlinearly smoothed majorisation-minimisation (NSMM) algorithm is derived from this perspective. An elegant representation of the NSMM algorithm is obtained using a novel projection-multiplication operator, a more precise monotonicity property of the algorithm is discovered, and the existence of a solution to the main optimisation problem is proved for the first time.

KEYWORDS:

• Mixture model
• penalised smoothed likelihood
• MM algorithm

Disclosure statement

No potential conflict of interest was reported by the authors.