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

Estimation of Gaussian mixtures in small sample studies using $l_1$ penalization