Robust Estimation of Dispersion Matrices and Principal Components

By Susan J. Devlin, R. Gnanadesikan, J. Kettenring. 1981

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Citations in the corpus

ANTIDOTE: understanding and defending against poisoning of anomaly detectors (2009, methodology): “In particular, there have been several approaches to developing robust PCA algorithms that construct a low dimensional subspace that captures most of the data’s dispersion(4) and are stable under data contamination [6, 7, 9, 19, 23].”
Robustness in Data Analysis: Criteria and Methods (2001, methodology): “The following estimators of a correlation matrix are studied: R the sample correlation matrix; RMVT the estimator based on the ellipsoidal multivariate trimming (Devlin et al., 1981); RAD the two-stage estimator with preliminary rejection of outliers by the adaptive algorithm and subsequent applying”
An Object-Oriented Framework for Robust Multivariate Analysis (2009, unknown): “Such an algorithm was proposed by Maronna and Zamar (2002) which is based on the very simple robust bivariate covariance estimator s jk proposed by Gnanadesikan and Kettenring (1972) and studied by Devlin et al. (1981).”
Behavior of Machine Learning Algorithms in Adversarial Environments (2010, methodology): “There have been two general approaches to make PCA robust: the first computes the principal components as the eigen-spectrum of a robust estimate of the covariance matrix [Devlin et al., 1981], while the second approach searches for directions that maximize a robust scale estimate of the data projec”
Robust Computation of Linear Models by Convex Relaxation (2012, methodology): “2 Robust Estimation of Covariance Matrix Another standard technique for robust PCA is to form a robust estimate of the covariance matrix of the data [19,22,24,39,54,55,79].”
The Regularized Iteratively Reweighted MAD Method for Change Detection in Multi- and Hyperspectral Data (2007, background): “Of course, other reweighting schemes for example leading to robust estimation [39], [40] of the variance–covariance structure of the data could be used.”
Structural equation modeling with heavy tailed distributions (2004, methodology): “Biases due to contamination of data like in this example is not uncommon in practical data analysis (see Devlin et al., 1981; Yuan & Bentler, 1998a).”
Applied Multivariate Analysis (2002, methodology): “However, we recommend using estimates obtained using the multivariate trimming (MVT) procedure of Gnanadesikan and Kettenring (1972) since Devlin et al. (1981) showed that the procedure is less sensitive to the number of extreme outliers, called the breakdown point.”
Inferences Based on a Skipped Correlation Coefficient (2004, background): “…associated with o has given rise to many alternative measures of association; see, for example, Huber (1981, p. 199), Ammann (1993), Davies (1987), Devlin et al. (1981), Goldberg & Iglewicz (1992), Kent & Tyler Correspondence Address: Rand R. Wilcox, Department of Psychology, University of…”
The Distribution of Robust Distances (2005, background): “The estimation of multivariate location and shape is one of the most difficult problems in robust statistics (Campell, 1980; Campell, 1982; Davies, 1987; Devlin et al., 1981; Donoho, 1982; Hampel et al., 1986; Huber, 1981; Lopuhaä, 1989; Maronna, 1976; Rocke and Woodruff, 1993; Rousseeuw, 1985; Rous”
Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution (2021, background): “Non-linear smoothing proposed by Devlin, Gnanadesikan and Kettenring Devlin, Gnanadesikan, and Kettenring (1975, 1981) proposed subtracting (or adding) a small constant value directly from (or to) the elements outside the diagonal of a correlation matrix that is NPD.”
Robust Estimates of Location and Dispersion for High-Dimensional Datasets (2002, background): “This collinearity is much higher than that in the simulations of Devlin et al. (1981) and Ma and Genton (2001).”