A robust distance-based approach for detecting multidimensional outliers

Identifying outliers in data analysis is a critical task, as outliers can significantly influence the results and conclusions drawn from a dataset. This study explores the use of the Mahalanobis distance metric for detecting outliers in multivariate data, focusing on a novel approach inspired by the work of M. Falk, [<i>On mad and comedians</i>, Ann. Inst. Stat. Math. 49 (1997), pp. 615-644]. The proposed method is rigorously tested through extensive simulation analysis, where it demonstrates high True Positive Rates (TPR) and low False Positive Rates (FPR) when compared to other existing outlier detection techniques. Through extensive simulation analysis, we empirically evaluate the affine equivariance and breakdown properties of our proposed distance measure and it is evident from the outputs that our robust distance measure demonstrates effective results with respect to the measures FPR and TPR. The proposed method was applied to seven different datasets, showing promising true positive rates (TPR) and false positive rates (FPR), and it outperformed several well-known outlier identification approaches. We can effectively use our proposed distance measure in fields demanding outlier detection.