no. 5
Statistiques
Robustifying multiple-set linear canonical analysis with S-estimator
[Robustification de l’analyse canonique linéaire généralisée avec un S-estimateur]
Bivigou, Ulrich Djemby1 ; Nkiet, Guy Martial1 
1 Université des Sciences et Techniques de Masuku, Franceville, Gabon
Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 571-576.

Dans cet article, nous considérons une version robuste de l’analyse canonique linéaire généralisée obtenue en utilisant un S-estimateur de l’opérateur de covariance. Les fonctions d’influence correspondantes sont déterminées. Les propriétés asymptotiques de cette méthode robuste sont obtenues, et un test robuste de non-corrélation mutuelle est introduit.

In this paper, we consider a robust version of multiple-set linear canonical analysis obtained by using a S-estimator of covariance operator. The related influence functions are derived. Asymptotic properties of this robust method are obtained and a robust test for mutual non-correlation is introduced.

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DOI : 10.5802/crmath.74
Bivigou, Ulrich Djemby 1 ; Nkiet, Guy Martial 1

1 Université des Sciences et Techniques de Masuku, Franceville, Gabon 
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Bivigou, Ulrich Djemby; Nkiet, Guy Martial. Robustifying multiple-set linear canonical analysis with S-estimator. Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 571-576. doi : 10.5802/crmath.74. http://www.numdam.org/articles/10.5802/crmath.74/

[1] Croux, Christophe; Dehon, Catherine nAalyse canonique basée sur des estimateurs robustes de la matrice des covariances, Rev. Stat. Appl., Volume 50 (2002), pp. 5-26

[2] Croux, Christophe; Filzmoser, Peter; Joossens, Kristel Classification efficiencies for robust linear discriminant analysis, Stat. Sin., Volume 18 (2008) no. 2, pp. 581-599 | MR | Zbl

[3] Croux, Christophe; Haesbroeck, Gentiane Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence function and efficiencies, Biometrika, Volume 87 (2000) no. 3, pp. 603-618 | DOI | MR | Zbl

[4] Davies, Patrick L. Asymptotic behaviour of S-estimates of multivariate location and parameters and dispersion matrices, Ann. Stat., Volume 15 (1987), pp. 1269-1292 | DOI | MR | Zbl

[5] Gardner, Sugnet; Gower, John C.; Le Roux, Niël J. A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis, Comput. Stat. Data Anal., Volume 50 (2006) no. 1, pp. 107-134 | DOI | MR | Zbl

[6] Gifi, Albert Nonlinear multivariate analysis, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, 1990 | MR | Zbl

[7] Hampel, Frank R.; Ronchetti, Elvezio M.; Rousseeuw, Peter J.; Stahel, Werner A. Robust Statistics: The Approach based on influence functions, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, 1986 | Zbl

[8] Hwang, Heungsun; Jung, Kwanghee; Takane, Yoshio; Woodward, Todd S. Functional multiple-set canonical correlation analysis, Psychometrika, Volume 77 (2012), pp. 753-775 | MR | Zbl

[9] Lopuhaä, Hendrik P. On the relation between S-estimator and M-estimator of multivariate location and covariance, Ann. Stat., Volume 17 (1989) no. 4, pp. 1662-1683 | DOI | MR | Zbl

[10] Lopuhaä, Hendrik P. Asymptotic expansion of S-estimators of location and covariance, Stat. Neerl., Volume 51 (1997) no. 2, pp. 220-237 | DOI | MR | Zbl

[11] Nkiet, Guy M. Asymptotic theory of multiple-set linear canonical analysis, Math. Methods Stat., Volume 26 (2017) no. 3, pp. 196-211 | DOI | MR | Zbl

[12] Takane, Yoshio; Hwang, Heungsun; Abdi, Hervé Regularized multiple-set canonical correlation analysis, Psychometrika, Volume 73 (2008) no. 4, pp. 753-775 | DOI | MR | Zbl

[13] Taskinen, Sara; Koch, Inge; Oja, Hannu Robustifying principal component analysis with spatial sign vectors, Stat. Probab. Lett., Volume 82 (2012) no. 4, pp. 765-774 | DOI | MR | Zbl

[14] Tenenhaus, Arthur; Tenenhaus, Michel Regularized generalized canonical correlation analysis, Psychometrika, Volume 76 (2011) no. 2, pp. 257-284 | DOI | MR | Zbl

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