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Robust Adaptive Estimation of Mean and Scatter Matrix in High‐Dimensional Settings

Jan Kalina & Marco Marozzi

International Statistical Review2026https://doi.org/10.1111/insr.70025article
AJG 3ABDC A
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0.50

Abstract

Summary Reliable estimation of the mean and the scatter matrix of multivariate data represent a fundamental task, particularly in high‐dimensional settings under the presence of outliers. This work is focused on robust estimation using the MWCD (minimum weighted covariance determinant) estimator and its regularised version (MRWCD estimator). Novel adaptive versions of the estimators are proposed together with a ‐sample extension, whose properties are evaluated through extensive simulations and a detailed analysis of real ‐sample data. These support the advantages of the newly proposed adaptive weights for the MRWCD estimator and illustrate its lower local sensitivity compared to a regularised version of the popular MCD estimator. An illustrative two‐group example demonstrates the advantage of the MRWCD estimator's adaptivity, showing how it clearly distinguishes group‐specific structure and robustly identifies outliers that standard methods may miss.

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https://doi.org/https://doi.org/10.1111/insr.70025

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@article{jan2026,
  title        = {{Robust Adaptive Estimation of Mean and Scatter Matrix in High‐Dimensional Settings}},
  author       = {Jan Kalina & Marco Marozzi},
  journal      = {International Statistical Review},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1111/insr.70025},
}

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