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. (Ann Stat 37(1):311–331, 2009) show 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. (TEST 24(3):441–461, 2015b) and Leung et al. (Comput Stat Data Anal 111:59–76, 2017), are special cases. We illustrate our method by using the half-space depth.

在经典的污染模型中，例如总误差（Huber和Tukey污染模型或逐案污染），观测值被视为要识别为异常值的单位。当考虑的变量数量适中时，此模型非常有用。Alqallaf等。（Ann Stat 37（1）：311–331，2009）展示了此方法对大量变量的局限性，并介绍了独立的污染模型（逐细胞污染），其中现在将细胞视为异常值单位或不。同时处理两种类型污染的一种方法是从数据集中过滤出受污染的细胞，然后应用能够处理个案异常值和缺失值的鲁棒程序。这里，我们开发了一个通用框架，可根据统计数据深度函数构建任何维度的过滤器。我们证明了以前的方法，例如Agostinelli等。（TEST 24（3）：441–461，2015b）和Leung等。（Comput Stat Data Anal 111：59–76，2017）是特例。我们通过使用半空间深度来说明我们的方法。