  The maximum likelihood principle is widely used in statistics, and the
associated estimators often display good properties. indeed maximum likelihood
estimators are guaranteed to be asymptotically efficient under mild conditions.
However in some settings, one has too few samples to get a good estimation. It
then becomes desirable to take into account prior information about the
distribution one wants to estimate. One possible approach is to extend the
maximum likelihood principle in a bayesian context, which then becomes a
maximum a posteriori estimate; however this requires a distribution model on
the distribution parameters. We shall therefore concentrate on the alternative
approach of regularized estimators in this paper; we will show how they can be
naturally introduced in the framework of maximum likelihood estimation, and how
they can be extended to form robust estimators which can reject outliers.
