Title: Cellwise and Casewise Robust Covariance in High Dimensions

Abstract:

While the sample covariance matrix serves as a fundamental component in multivariate statistics, it is notoriously vulnerable to outlier contamination. Such anomalies manifest either as casewise outliers—representing observations drawn from a distinct population—or as cellwise outliers, which involve individual deviating entries within the data matrix. Although recent advancements have yielded robust covariance estimators capable of addressing both outlier types, their computational feasibility is currently restricted to datasets with no more than 20 dimensions. To address this limitation, we introduce cellRCov, a robust covariance estimator designed to concurrently manage casewise outliers, cellwise outliers, and missing values. This approach is grounded in a covariance decomposition across principal and orthogonal subspaces, incorporating insights from recent developments in robust Principal Component Analysis (PCA). Additionally, a ridge-type regularization technique is applied to ensure the stability of the resulting covariance estimate. We outline key theoretical attributes of cellRCov, covering its casewise and cellwise influence functions, alongside proofs of consistency and asymptotic normality. Simulation experiments highlight cellRCov’s enhanced performance in scenarios involving data contamination and missingness. The method’s practical effectiveness is further demonstrated through a real-world case study focused on anomaly detection. Finally, we present cellRCCA, a method for robust and regularized canonical correlation analysis, and provide illustrative examples of its application.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC