Robust Statistics: Theory and Methods

By Danece Sauve. 2006

2,170 citations recorded by the source corpus.

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Citations in the corpus

Robust Aggregation for Federated Learning (2019, methodology): “We adopt this approach to federated learning by considering a classical multidimensional generalization of the median, known variously as the geometric or spatial or L1 median [65].”
Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learning (2018, methodology): “treatments consider the robustness of learning to noise, including the extension of the PAC model by Kearns and Li [31], as well as work on robust statistics [8], [28], [52], [56].”
The security of machine learning (2010, methodology): “We have put our framework to use studying attacks against the SpamBayes statistical spam filter [Nelson et al., 2008]. Here we review that work and demonstrate how our framework informs and structures the analysis. SpamBayes is a content-based statistical spam filter that classifies email using toke”
Security Evaluation of Support Vector Machines in Adversarial Environments (2014, background): “This has been also studied from a more theoretical perspective in [23], exploiting the framework of Robust Statistics [35, 50].”
Robustness and Regularization of Support Vector Machines (2008, background): “An alternative interpretation of robustness stems from the rich literature on Robust Statistics (e.g., Huber, 1981; Hampel et al., 1986; Rousseeuw and Leeroy, 1987; Maronna et al., 2006), which studies how an estimator or algorithm behaves under a small perturbation of the statistics model.”
The forward search: theory and data analysis (2010, background): “As we emphasized at the end of the Introduction, a crucial advantage of the forward search over alternative robust approaches (Maronna et al., 2006) is that the main principles are readily extended to any data analysis context, with only minor changes in the implementation reflecting the technicalit”
Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score (2018, neutral): “[36] Maronna, R.”
Outlier identification in high dimensions (2008, background): “The translated biweight fits into the general framework of S-estimators described by equation (4) and is similar to Tukey’s biweight function except that ψ starts rising from 0 at some point M from the origin.”
Statistical guidelines for Apis mellifera research (2013, background): “A recent reference on robust statistics is Maronna et al. (2006), while the classic one is Huber (1981).”
Elliptical graphical modelling (2011, background): “There are many aﬃne equivariant, robust estimators, see, for example, Zuo (2006) or Maronna et al. (2006).”
Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation (2010, background): “See Maronna, Martin, and Yohai (2006) for general discussion.”
Complex Elliptically Symmetric Distributions: Survey, New Results and Applications (2012, background): “The real elliptically symmetric (RES) distributions have become a standard part of multivariate analysis and results for RES distributions are incorporated into most multivariate analysis textbooks [11], [40], [62] and textbooks on robust multivariate statistics [37], [60].”
A robust coefficient of determination for regression (2010, background): “Given then a choice for the ρ-function, Maronna et al. (2006), p. 171, propose a robust equivalent for the R2 (4) given by R2ρ = 1− ∑n i=1 ρ ( yi−xTi β̂ σ̂ ) ∑n i=1 ρ ( yi−µ̂ σ̂ ) (8) where µ̂ is a robust location estimate of E(y), solution of min µ n∑ i=1 ρ ( yi − µ σ̂ ) (9) and β̂ and σ̂ are…”
Robust Estimation for ARMA models (2009, methodology): “One possibility to explore is to adapt to ARMA models the robust finite prediction error (RFPE) selection criterion given in Section 5.12 of Maronna, Martin and Yohai [16] for regression.”
Anomaly detection by robust statistics (2017, background): “This aspect is studied in 3,7 and in other works they reference.”