A further study comparing forward search multivariate outlier methods including ATLA with an application to clustering

Abstract

This paper makes comparisons of automated procedures for robust multivariate outlier detection through discussion and simulation. In particular, automated procedures that use the forward search along with Mahalanobis distances to identify and classify multivariate outliers subject to predefined criteria are examined. Procedures utilizing a parametric model criterion based on a $$\chi ^2$$ χ 2 -distribution are among these, whereas the multivariate Adaptive Trimmed Likelihood Algorithm (ATLA) identifies outliers based on an objective function that is derived from the asymptotics of the location estimator assuming a multivariate normal distribution. Several criterion including size (false positive rate), sensitivity, and relative efficiency are canvassed. To illustrate relative efficiency in a multivariate setting in a new way, measures of variability of the multivariate location parameter when the underlying distribution is chosen from a multivariate generalization of the Tukey–Huber $$\epsilon $$ ϵ -contamination model are used. Mean slippage models are also entertained. The simulation results here are illuminating and demonstrate there is no broadly accepted procedure that outperforms in all situations, albeit one may ascertain circumstances for which a particular method may be best if implemented. Finally the paper explores graphical monitoring for existence of clusters and the potential of classification through occurrence of multiple minima in the objective function using ATLA.

Visualisation of Mahalanobis Distances for Trivariate JOINT Distributions

“…The Mahalanobis distance has also found applications in finance, including asset classification (Zuo and Serfling, 2000), portfolio surveillance (Kritzman and Li, 2010), and outlier frequency and severity detection (Penny, 1996;Ghorbani, 2019;Li et al, 2019;Clarke and Grose, 2023;Singh et al, 2023). Its usefulness in the identification of multivariate outliers arises from its selection of robust and independent centroid and covariance matrix measures.…”