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The aim is to establish a robust estimation method for multivariate data affected by contamination using heavy-tailed distributions.

February 22, 2026Statistics and ComputingOpen Access

Robust distances and multivariate outlier detection under heavy tails

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The aim is to establish a robust estimation method for multivariate data affected by contamination using heavy-tailed distributions.
Develop a unified approach utilizing high-breakdown estimation for multivariate Student-t distribution.
Obtain influence functions for robust Mahalanobis distances.
Introduce new statistics for assessing conformance to the multivariate Student-t distribution.
Design an automatic procedure for estimating degrees of freedom and contamination rates.
Address computational challenges in Monte Carlo estimation of quantiles.
The proposed method provides accurate robust estimation under contamination scenarios.
Simulation evidence validates the effectiveness and replicability of the new algorithms.
New statistical measures demonstrate robustness in estimating location, scatter, and tail parameters.

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This work develops a unified approach for robust estimation under contamination in multivariate data, suggesting methods and algorithms.

Barabesi et al. (2026) studied this question.

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