Robust Estimates of Location and Dispersion for High-Dimensional Datasets

By Ricardo A. Maronna, Ruben H. Zamar. Technometrics, 2002

439 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ba8f7111cacec9e7eb13f40f9abf369444172962

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

High-Breakdown Inference for Mixed Linear Models (2006, background): “The data that we have come from an experiment in which subjects had to decide as quickly as possible whether a target (object’s drawing) appearing after a prime (action of a pantomime) was a real object or not (see Moy and Mounoud 2003).”
Robust Multivariate Analysis (2017, methodology): “Maronna and Zamar (2002) modify this idea to create a fairly fast (possibly high breakdown consistent) OGK estimator of multivariate location and dispersion.”
Robust Estimation Using the Huber Function With a Data-Dependent Tuning Constant (2007, background): “However, this can be computationally challenging because finding “good” initial values are essential for these estimation procedures especially for high-dimensional datasets (Campbell, Lopuhaä, and Rousseeuw 1998; Maronna and Zamar 2002).”
Robust linear regression for high‐dimensional data: An overview (2020, positive): “There are, however, covariance estimators which also work in the high-dimensional situation (Hubert, Rousseeuw, & Van den Branden, 2005; Maronna & Zamar, 2002), and methods based on the principle of projection pursuit (Croux, Filzmoser, & Oliveira, 2007; Croux & Ruiz-Gazen, 2005).”
Outlier Detection for Compositional Data Using Robust Methods (2008, background): “The idea of (a) is to repeatedly project the multivariate data to the univariate space, because univariate outlier detection is much simpler (Gnanandesikan and Kettenring, 1972; Peña and Prieto, 2001; Maronna and Zamar, 2002).”
Outlier identification in high dimensions (2008, methodology): “Maronna and Zamar (2002) note that the robust distances d can be quickly computed in the eigenvector space without the need for matrix inversion since the p components are orthogonal in this space.”
Robust High-Dimensional Precision Matrix Estimation (2014, methodology): “To this end, they use the orthogonalized GnanadesikanKettenring (OGK) approach [Maronna and Zamar, 2002] as well as the computation of the nearest positive (semi)definite (NPD) matrix as suggested by Higham [2002].”
Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation (2010, methodology): “For example, a method based on pairwise robust covariance estimation was proposed by Gnanadesikan and Kettenring (1972) and later modified by Maronna and Zamar (2002).”
Elliptical graphical modelling (2011, background): “One way to circumvent this problem is to drop the affine equivariance and resort to robust “pairwise” estimators, such as the Gnanadesikan-Kettenring estimator (Gnanadesikan and Kettenring, 1972; Maronna and Zamar, 2002) or marginal sign and rank matrices (Visuri et al.”
Influence functions of the Spearman and Kendall correlation measures (2010, background): “However, robust correlation measures can be used to construct multivariate covariance matrices, based on pairwise covariances (see Gnanadesikan and Kettering 1972, and Maronna and Zamar 2002 ).”