Robust Multivariate Estimation Based On Statistical Depth Filters

TL;DR

This paper introduces a general framework for robust multivariate estimation using statistical depth filters, capable of handling both cell-wise and case-wise contamination in high-dimensional data.

Contribution

It develops a flexible, depth-based filtering approach that generalizes previous methods to effectively manage various contamination types in multivariate datasets.

Findings

The proposed method effectively detects outliers in high-dimensional data.

It generalizes existing approaches using statistical depth functions.

Illustrated with half-space depth, demonstrating practical applicability.

Abstract

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.