  Multivariate location and scatter matrix estimation is a cornerstone in
multivariate data analysis. We consider this problem when the data may contain
independent cellwise and casewise outliers. Flat data sets with a large number
of variables and a relatively small number of cases are common place in modern
statistical applications. In these cases global down-weighting of an entire
case, as performed by traditional robust procedures, may lead to poor results.
We highlight the need for a new generation of robust estimators that can
efficiently deal with cellwise outliers and at the same time show good
performance under casewise outliers.
