Case-Wise and~Cell-Wise Outliers Detection Based on~Statistical Depth Filters

According to the classical case-wise contamination model, observations are considered as the units to be identified as outliers. Alqallaf et al. (2009) showed the limits of this approach, especially for a larger number of variables, and introduced the Independent contamination model, or cell-wise contamination, where the cells are the units to be identified as outliers. For the estimation problem, 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. In this work we deal with the outliers detection task, taking into account both types of contamination. We propose to use the depth filters introduced by Agostinelli (2021) as detection procedure which is able to identify both case-wise and cell-wise outliers. We investigated the finite sample performance by a small simulation study, comparing the depth filters with the detection rules available in literature.