Robust Outlier Detection for High-Dimensional Interval-Valued Data (Appendix)

Experiment 1.1 conducts outlier detection experiments for low-dimensional and moderately high-dimensional interval-valued data, evaluating the proposed method when the covariance matrix can be estimated directly or regularized. Experiment 1.2 conducts outlier detection experiments for high-dimensional interval-valued data, examining the applicability and robustness of the proposed method when (p \geq 2n) and the covariance matrix is singular.

Experiment 1.3 provides comparative experiments under different contamination proportions and outlier types, testing the method’s ability to detect center outliers, range outliers, and mixed outliers. The evaluated methods include traditional Mahalanobis-distance-based approaches, robust covariance estimation methods, and the proposed high-dimensional interval-valued outlier detection method based on modified Mahalanobis distance and a BH-FDR adaptive threshold.