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Donoho D. L. (1982) Breakdown properties of multivariate location estimators

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Donoho D. L. (1982) Breakdown properties of multivariate location estimators are crucial for robust estimation. Various high-breakdown-point estimators, such as the MM-estimator with smooth hard rejection and the Rocke S-estimator, are designed for efficiency at the Gaussian distribution but can lack efficiency in non-Gaussian scenarios. A new S-q estimator is proposed for symmetric elliptical distributions, offering higher maximum efficiency across common families like Gaussian, t-, Cauchy distributions while maintaining a high breakdown point. Additionally, the S-q estimator demonstrates robustness comparable to leading estimators and stability with initial conditions, making it broadly applicable for practitioners. This advancement in multivariate location estimation is exemplified in financial portfolio optimization, showcasing the practical utility of the S-q estimator.

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Journal Article•DOI Affine-equivariant inference for multivariate location under Lp loss functions Alexander Dürre, Davy Paindaveine - Show less +1 more 01 Oct 2022-Annals of Statistics	The paper discusses affine-equivariant multivariate location estimators under Lp loss functions, providing asymptotic properties and equivariance under afﬁne transformations, but does not address Donoho's breakdown properties.
Open access•Journal Article•DOI New highly efficient high‐breakdown estimator of multivariate scatter and location for elliptical distributions 16 Apr 2023-Canadian Journal of Statistics-revue Canadienne De Statistique	The paper introduces a new S-q estimator for multivariate scatter and location with high efficiency and breakdown point, surpassing existing estimators for elliptical distributions.
Open access•Posted Content New Highly Efficient High-Breakdown Estimator of Multivariate Scatter and Location for Elliptical Distributions Justin A. Fishbone, Lamine Mili - Show less +1 more 31 Aug 2021-arXiv: Statistics Theory	The paper introduces a new S-q estimator with high efficiency and maximum breakdown point for multivariate scatter and location estimation in elliptical distributions, surpassing existing estimators.
Patent Multivariate position estimation Wilden Jason 16 Feb 2021	Not addressed in the paper.

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