Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices

By Hendrik P. Lopuhaä, Peter J. Rousseeuw. 1991

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Citations in the corpus

Distributed Statistical Machine Learning in Adversarial Settings (2017, background): “It is shown in [18] that geometric median has a breakdown point of 0.”
A robust PCR method for high‐dimensional regressors (2003, background): “In Reference [15], however, it is mentioned that the performance of reweighted S-estimators of location and covariance [18] did not benefit from using this biweight function, hence the authors recommended the use of hard rejection.”
The multivariate least-trimmed squares estimator (2008, unknown): “1 in [16] we obtain min(̂LS(H2)) = min(cov({yj − Bt 2xj ; j ∈ H2})) k(Zn) + 1 h min(Cov0({yj − Bt 2xj ; j ∈ J̄ })) k(Zn) + 1 h c2(J̄ ) k(Zn) + 1 h c.”
Central limit theorem and influence function for the MCD estimators at general multivariate distributions (2009, unknown): “ST/0907.0079”
A comparison of robust alternatives to Hotelling’s T 2 control chart (2009, methodology): “A fast algorithm was proposed independently by Hawkins and Olive [12] and Rousseeuw and Van Driessen [25].”
Distributed Linearized Alternating Direction Method of Multipliers for Composite Convex Consensus Optimization (2015, background): “This computational setting, i.e., decentralized consensus optimization, appears as a generic model for various applications in signal processing, e.g., [2]–[6], machine learning, e.g., [7]–[9] and statistical inference, e.g., [10], [11].”
MULTIVARIATE REGRESSION S-ESTIMATORS FOR ROBUST ESTIMATION AND INFERENCE (2005, result): “This result extends the results for multivariate location and scatter given by Lopuhaä and Rousseeuw (1991) and the results for univariate regression given by Rousseeuw and Yohai (1984). Theorem 1.”
Semi-parametric modelling in finance: theoretical foundations (2002, background): “For background, see e.g. Lopuhaä and Rousseeuw (1991), Lopuhaä (1999).”
Sign and rank covariance matrices (2000, methodology): “See Maronna (1976), Huber (1977), Campbell (1980) and Kent and Tyler (1991) for M -estimates and Davies (1987), Lopuhaä (1989) and Lopuhaä and Rousseeuw (1991) for so called S-estimates.”