High breakdown estimators for principal components: the projection-pursuit approach revisited

By Christophe Croux, Anne Ruiz-Gazen. 2005

345 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b3e596c82d94117962ca4d2ba3fed81d6060d1c9

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In Statistics and Probability

Citations in the corpus

Rainbow Plots, Bagplots, and Boxplots for Functional Data (2010, methodology): “Because principal component decomposition is not resistant to outliers, we apply Croux and Ruiz-Gazen’s (2005) robust principal component algorithm, which uses a form of projection pursuit.”
ROBPCA: A New Approach to Robust Principal Component Analysis (2005, methodology): “More attractive methods have been developed in Croux and Ruiz-Gazen (2000), but in high dimensions, these algorithms still have a numerical inaccuracy.”
Robust functional principal components: A projection-pursuit approach (2011, methodology): “…important when estimating principal components in the finite-dimensional setting, since as it was pointed out by Cui, He and Ng (2003) and Croux and Ruiz-Gazen (2005) the variances of some elements of the estimated principal directions may blow up when using the mad leading to highly…”
Robust linear regression for high‐dimensional data: An overview (2020, neutral): “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).”
Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap (2006, methodology): “Consequently, several robustifications of classical PCA have been proposed in the literature, including projection-pursuit ap proaches (Li and Chen 1985; Croux and Ruiz-Gazen 2005; Hubert, Rousseeuw, and Verboven 2002) and the use of robust estimators of scatter instead of the sample covariance. The”
High-Breakdown Robust Multivariate Methods (2008, methodology): “The Stahel– Donoho estimator measures the outlyingness by looking at all univariate projections of the data and as such is related to projection pursuit methods as studied in Friedman and Tukey (1974), Huber (1985) and Croux and Ruiz-Gazen (2005).”
Randomized Matrix Decompositions using R (2016, methodology): “These techniques are concerned with computing robust estimators for the empirical covariance matrix, for instance, see the seminal work by Hubert, Rousseeuw, and Vanden Branden (2005) and Croux and Ruiz-Gazen (2005).”
An Object-Oriented Framework for Robust Multivariate Analysis (2009, neutral): “A more tractable algorithm in these lines was ﬁrst proposed by Croux and Ruiz-Gazen (1996) and later improved by Croux and Ruiz-Gazen (2005).”
Robust statistics in data analysis — A review: Basic concepts (2007, methodology): “Another robust method was described by Croux and RuizGazen [50,51], who exploits the idea of Projection Pursuit applying robust measure of the data scale as a projection pursuit criterion.”
Properties of design-based functional principal components analysis (2008, methodology): “Let us remark that the influence functions of the eigenelements are similar to those found in the multivariate framework for classical PCA (Croux and Ruiz-Gazen, 2005).”