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

Brenton R. Clarke () and Andrew Grose
Additional contact information
Brenton R. Clarke: Murdoch University
Andrew Grose: Curtin University

Statistical Papers, 2023, vol. 64, issue 2, No 2, 395-420

Abstract: 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.

Keywords: Efficiency; Forward search; Mahalanobis distance; Minimum covariance determinant estimator; Monte Carlo simulation; Multivariate normal distribution; 62F35; 62H12 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00362-022-01319-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01319-7

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-022-01319-7

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().