  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 nonlinearly smoothed majorization-minimization (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 optimization problem is proved for the first time.
