  In this manuscript, we consider a finite multivariate nonparametric mixture
model where the dependence between the marginal densities is modeled using the
copula device. Pseudo EM stochastic algorithms were recently proposed to
estimate all of the components of this model under a location-scale constraint
on the marginals. Here, we introduce a deterministic algorithm that seeks to
maximize a smoothed semiparametric likelihood. No location-scale assumption is
made about the marginals. The algorithm is monotonic in one special case, and,
in another, leads to ``approximate monotonicity'' -- whereby the difference
between successive values of the objective function becomes non-negative up to
an additive term that becomes negligible after a sufficiently large number of
iterations. The behavior of this algorithm is illustrated on several simulated
datasets. The results suggest that, under suitable conditions, the proposed
algorithm may indeed be monotonic in general. A discussion of the results and
some possible future research directions round out our presentation.
