Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies

By Christophe Croux, G. Haesbroeck. 2000

379 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e6a1ca6f64055d5302cb7612cb61b295ee0d62e1

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In Analytical Chemistry

In Statistics and Probability

Citations in the corpus

Application of PCA, SVR, and ANFIS for modeling of rock fragmentation (2015, methodology): “PCA is a classical method that provides a sequence of the best linear approximations to a given high-dimensional observation, and it has received much more attentions in many literatures (Cadima and Jolliffe 1995; Croux and Haesbroeck 2000; Higuchi and Eguchi 2004; Shawe-Taylor and Cristianini 2005;”
Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices (2006, background): “Lemma 1 in Croux and Haesbroeck (2000) states that, for any scatter functional C(F), there exist two real valued functions J'c(r) and 6c (r) such that the influence function of C at a spherical Fa, symmetric around the origin and with C(Fo) = h, is given by”
A canonical definition of shape (2008, neutral): “, (4) and ∆ θS ,f1;3 := 1 2 √ n M VS S (”
Nearest-Neighbor Variance Estimation (NNVE) (2002, methodology): “It is then possible to obtain limit results for multivariate analysis procedures based on robust covariance matrix estimators, as was done in the context of principal components (Croux and Haesbroeck 2000), multivariate regression (Rousseeuw, Van Aelst, and Van Driessen 2000),”
Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap (2006, methodology): “In the multivariate situation, S estimators become more efficient with increasing dimension (see, e.g., Croux and Haesbroeck 1999; Lopuha?”
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].”
An Object-Oriented Framework for Robust Multivariate Analysis (2009, methodology): “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). To improve the performance of the algorithm for high dimensional data a new improved version was proposed by Croux et al.”
Robust estimation of Cronbach's alpha (2006, methodology): “…based on robust estimation of location and scatter have been developed and investigated such as factor analysis (Pison et al. 2002a), principal component analysis (Croux and Haesbroeck 2000), canonical correlation analysis (Croux and Dehon 2001) and multivariate regression (Rousseeuw et al. 2001).”