Comparative study of test on covariance performance in two outlier scenarios.

In practice, multivariate data frequently include outliers. Since outliers can cause incorrect conclusions, a robust estimator must be used to analyze the data as the robust estimator is designed to be resistant to outliers. One of the latest robust estimators for multivariate data is the Test on Covariance (TOC). The performance of TOC has been investigated via simulation studies and historical datasets in few studies. The simulation studies from past researchers used two outlier scenarios, mean shift (Outlier Scenario 1) and covariance shift (Outlier Scenario 2). However, the focus of previous studies is on the number of variables, p ≤ 5 with small to large sample sizes and percentage of outliers ranging from 1% to 25% only. Thus, the objective of this study is to investigate further the performance of TOC with existing robust estimators in these two outliers' scenarios, however focusing on the number of variables, p ≥ 5, small and moderate sample sizes, and percentage of outliers ranging from 5% to 25%. Measurements used to evaluate the performance of TOC and the existing robust estimators are pout, pmask, and pswamp. The pout is the probability of all outliers successfully detected, pmask is the probability of masking effect, and pswamp is the probability of swamping effect. It is found that, TOC exhibits better results in Outlier Scenario 1 than Outlier Scenario 2, especially when the separation between outliers and inliers is large for pout and pmask. However, the performance of TOC is excellent in both outlier scenarios for pswamp as TOC shows the lowest probability of swamping. [ABSTRACT FROM AUTHOR]