  In the classical contamination models, such as the gross-error (Huber and
Tukey contamination model or Case-wise Contamination), observations are
considered as the units to be identified as outliers or not. This model is very
useful when the number of considered variables is moderately small. Alqallaf et
al. [2009] shows the limits of this approach for a larger number of variables
and introduced the Independent contamination model (Cell-wise Contamination)
where now the cells are the units to be identified as outliers or not. One
approach to deal, at the same time, with both type of contamination is filter
out the contaminated cells from the data set and then apply a robust procedure
able to handle case-wise outliers and missing values. Here we develop a general
framework to build filters in any dimension based on statistical data depth
functions. We show that previous approaches, e.g. Agostinelli et al. [2015a]
and Leung et al. [2017], are special cases. We illustrate our method by using
the half-space depth.
