Simulation Study of the Test on Covariance Estimator for Outlier Detection in Multivariate Data with Mean and Covariance Shifts

Outlier detection in multivariate data is complex compared to univariate data, which can be done using graphical inspection. Outlier detection is also one of the common issues in multivariate analysis and has been applied to tax fraud detection and industrial food inspection. Outliers’ studies are closely related to robust estimators of the sample mean and covariance matrix as these estimators are resistant toward outliers. The Test on Covariance (TOC) is a newly developed robust estimator for multivariate data. Until now, TOC’s performance was investigated for two outlier scenarios by shifting the mean and covariance separately. TOC shows good results in both outlier scenarios and is found to be applicable in detecting outliers. In this study, the performance of TOC is investigated further in detecting outliers via simulation study for other outliers’ scenarios by shifting the mean and covariance simultaneously. Other robust estimators; Fast Minimum Covariance Determinant (FMCD), Minimum Vector Variance (MVV), Covariance Matrix Equality (CME) and Index Set Equality (ISE) are used as a comparison. Various conditions of sample sizes, number of variables, and percentage of outliers, are considered in the simulation study. The performance of all robust estimators is measured by probability to detect outliers (pout), masking error (pmask) and swamping error (pswamp). Results present that the TOC can be the best robust estimator, give the same performance as other robust estimators in detecting outliers, and have a low masking error when outliers and inliers are far from each other. Moreover, TOC displays good results in low swamping errors for most cases which means TOC has a low probability of misclassifying inliers as outliers compared to other robust estimators. In conclusion, TOC is an applicable and promising approach for outlier detection in multivariate data and can be incorporated with other multivariate analyses.