  Many experiments in medicine and ecology can be conveniently modeled by
finite Gaussian mixtures but face the problem of dealing with small data sets.
We propose a robust version of the estimator based on self-regression and
sparsity promoting penalization in order to estimate the components of Gaussian
mixtures in such contexts. A space alternating version of the penalized EM
algorithm is obtained and we prove that its cluster points satisfy the
Karush-Kuhn-Tucker conditions. Monte Carlo experiments are presented in order
to compare the results obtained by our method and by standard maximum
likelihood estimation. In particular, our estimator is seen to perform better
than the maximum likelihood estimator.
