  A novel approach to obtain weighted likelihood estimates of multivariate
location and scatter is discussed. A weighting scheme is proposed that is based
on the distribution of the Mahalanobis distances rather than the distribution
of the data at the assumed model. This strategy allows to avoid the curse of
dimensionality affecting non-parametric density estimation, that is involved in
the construction of the weights through the Pearson residuals Markatou et al
(1998). Then, weighted likelihood based outlier detection rules and robust
dimensionality reduction techniques are developed. The effectiveness of the
methodology is illustrated through some numerical studies and real data
examples.
