  We propose a general approach to construct weighted likelihood estimating
equations with the aim of obtain robust estimates. The weight, attached to each
score contribution, is evaluated by comparing the statistical data depth at the
model with that of the sample in a given point. Observations are considered
regular when the ratio of these two depths is close to one, whereas, when the
ratio is large the corresponding score contribution may be downweigthed.
Details and examples are provided for the robust estimation of the parameters
in the multivariate normal model. Because of the form of the weights, we expect
that, there will be no downweighting under the true model leading to highly
efficient estimators. Robustness is illustrated using two real data sets.
