Multivariate estimation with high breakdown point

By Peter J. Rousseeuw. 1985

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Citations in the corpus

The Hidden Vulnerability of Distributed Learning in Byzantium (2018, background): “While we know from (Rousseeuw, 1985) that the Median has an optimal breakdown of 0 .”
Breakdown and groups (2005, background): “Proof: The proof of the theorem follows the lines of Rousseeuw (1983, 1984) and Davies (1987, 1993).”
Multivariate outlier detection in exploration geochemistry (2005, unknown): “However, d. ARTICLE IN PRESS”
The largest nonindentifiable outlier: a comparison of multivariate simultaneous outlier identification rules (2001, methodology): “1) by simulation using the algorithms of Rousseeuw and van Driessen (1999) and Rousseeuw and van Zomeren (1990), as implemented in the statistical package S-Plus (version 4.”
Outlier detection using distributionally robust optimization under the Wasserstein metric (2017, methodology): “ vulnerable to outliers. The most commonly used robust regression techniques, including M-estimation [Huber, 1964, 1973], Least Median of Squares (LMS) [Rousseeuw, 1984], Least Trimmed Squares (LTS) [Rousseeuw, 1985], S-estimation [Rousseeuw and Yohai, 1984], and MM-estimation [Yohai, 1987], are ela”
Robust Estimates of Location and Dispersion for High-Dimensional Datasets (2002, background): “Some of them are based on the minimization of a robust scale of Mahalanobis distances: the minimum volume ellipsoid (MVE) and minimum covariance determinant (MCD) estimates (Rousseeuw 1984, 1985), S estimates (Davies 1987), and ’ estimates (Lopuha¨a 1991).”
Identification of Multivariate Outliers: A Performance Study (2016, methodology): “The increasing size of data sets makes it more and more difficult to identify common structures in the data.”
Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation (2010, methodology): “A more straightforward approach is to use the quantities (38), but as modified by a SICS transformation, and employing a univariate outlyingness function O(x, F ) satisfying the assumptions of Theorem 6.”
High breakdown estimators for principal components: the projection-pursuit approach revisited (2005, methodology): “As such, the Minimum Volume Ellipsoid estimator (Rousseeuw 1985) was used by Naga and Antille (1990).”
Breakdown points of trimmed likelihood estimators and related estimators in generalized linear models (2003, methodology): “This restriction was also used in the approaches of Rousseeuw (1984, 1985) and Rousseeuw and Leroy (1987) concerning”
Robust statistics for outlier detection (2011, background): “11 , 12 The MCD looks for those h observations in the data set (where the number h is given by the user) whose classical covariance matrix has the lowest possible determinant.”