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Volumn 82, Issue 4, 2012, Pages 765-774

Robustifying principal component analysis with spatial sign vectors

Author keywords

Affine equivariance; Efficiency; Influence function; Robustness; Spatial sign vector

Indexed keywords


EID: 84856045016     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2012.01.001     Document Type: Article
Times cited : (30)

References (24)
  • 1
    • 0001699986 scopus 로고
    • Asymptotic theory for principal component analysis
    • Anderson T.W. Asymptotic theory for principal component analysis. Ann. Math. Statist. 1963, 34:122-148.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 122-148
    • Anderson, T.W.1
  • 3
    • 0001088628 scopus 로고    scopus 로고
    • Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies
    • Croux C., Haesbroeck G. Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 2000, 87:603-618.
    • (2000) Biometrika , vol.87 , pp. 603-618
    • Croux, C.1    Haesbroeck, G.2
  • 4
    • 0242420673 scopus 로고    scopus 로고
    • Sign and rank covariance matrices: statistical properties and application to principal components analysis
    • Birkhauser, Basel, Y. Dodge (Ed.)
    • Croux C., Ollila E., Oja H. Sign and rank covariance matrices: statistical properties and application to principal components analysis. Statistical Data Analysis Based on the L1-Norm and Related Methods 2002, 257-271. Birkhauser, Basel. Y. Dodge (Ed.).
    • (2002) Statistical Data Analysis Based on the L1-Norm and Related Methods , pp. 257-271
    • Croux, C.1    Ollila, E.2    Oja, H.3
  • 6
    • 7744247580 scopus 로고    scopus 로고
    • On Tyler's M-functional of scatter in high dimension
    • Dümbgen L. On Tyler's M-functional of scatter in high dimension. Ann. Inst. Statist. Math. 1998, 50:471-491.
    • (1998) Ann. Inst. Statist. Math. , vol.50 , pp. 471-491
    • Dümbgen, L.1
  • 7
    • 19744368600 scopus 로고    scopus 로고
    • On the breakdown properties of some multivariate M-functionals
    • Dümbgen L., Tyler D. On the breakdown properties of some multivariate M-functionals. Scandinavian J. Statist. 2005, 32:247-264.
    • (2005) Scandinavian J. Statist. , vol.32 , pp. 247-264
    • Dümbgen, L.1    Tyler, D.2
  • 8
    • 64249133685 scopus 로고    scopus 로고
    • Asymptotic distributions of robust shape matrices and scales
    • Frahm G. Asymptotic distributions of robust shape matrices and scales. J. Multivariate Anal. 2009, 100:1329-1337.
    • (2009) J. Multivariate Anal. , vol.100 , pp. 1329-1337
    • Frahm, G.1
  • 9
    • 50949086005 scopus 로고    scopus 로고
    • Robust functional estimation using the spatial median and spherical principal components
    • Gervini D. Robust functional estimation using the spatial median and spherical principal components. Biometrika 2008, 95:587-600.
    • (2008) Biometrika , vol.95 , pp. 587-600
    • Gervini, D.1
  • 11
    • 24944574513 scopus 로고    scopus 로고
    • A practical affine equivariant multivariate median
    • Hettmansperger T.P., Randles R.H. A practical affine equivariant multivariate median. Biometrika 2003, 89:851-860.
    • (2003) Biometrika , vol.89 , pp. 851-860
    • Hettmansperger, T.P.1    Randles, R.H.2
  • 13
    • 0033565077 scopus 로고    scopus 로고
    • Some robust estimates of principal components
    • Marden J.I. Some robust estimates of principal components. Statist. Probab. Lett. 1999, 43:349-359.
    • (1999) Statist. Probab. Lett. , vol.43 , pp. 349-359
    • Marden, J.I.1
  • 14
    • 80051509836 scopus 로고    scopus 로고
    • Multivariate L1 methods: the package MNM
    • Nordhausen K., Oja H. Multivariate L1 methods: the package MNM. J. Stat. Softw. 2011, 43:1-28.
    • (2011) J. Stat. Softw. , vol.43 , pp. 1-28
    • Nordhausen, K.1    Oja, H.2
  • 16
    • 18844444483 scopus 로고    scopus 로고
    • Multivariate nonparametric tests
    • Oja H., Randles R. Multivariate nonparametric tests. Statist. Sci. 2004, 19:598-605.
    • (2004) Statist. Sci. , vol.19 , pp. 598-605
    • Oja, H.1    Randles, R.2
  • 17
    • 50649097697 scopus 로고    scopus 로고
    • A canonical definition of shape
    • Paindaveine D. A canonical definition of shape. Statist. Probab. Lett. 2008, 78:2240-2247.
    • (2008) Statist. Probab. Lett. , vol.78 , pp. 2240-2247
    • Paindaveine, D.1
  • 19
    • 0001648921 scopus 로고
    • Sensitivity analysis in principal component analysis: influence on the subspace spanned by principal component
    • Tanaka Y. Sensitivity analysis in principal component analysis: influence on the subspace spanned by principal component. Commun. Stat. 1988, 17:3157-3175.
    • (1988) Commun. Stat. , vol.17 , pp. 3157-3175
    • Tanaka, Y.1
  • 20
    • 29444449787 scopus 로고    scopus 로고
    • Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
    • Taskinen S., Croux C., Kankainen A., Ollila E., Oja H. Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices. J. Multivariate Anal. 2006, 97:359-384.
    • (2006) J. Multivariate Anal. , vol.97 , pp. 359-384
    • Taskinen, S.1    Croux, C.2    Kankainen, A.3    Ollila, E.4    Oja, H.5
  • 21
    • 0000342767 scopus 로고
    • A distribution-free M-estimator of multivariate scatter
    • Tyler D.E. A distribution-free M-estimator of multivariate scatter. Ann. Statist. 1987, 15:234-251.
    • (1987) Ann. Statist. , vol.15 , pp. 234-251
    • Tyler, D.E.1
  • 22
    • 77954533745 scopus 로고    scopus 로고
    • A note on multivariate location and scatter statistics for sparse data sets
    • Tyler D.E. A note on multivariate location and scatter statistics for sparse data sets. Statist. Probab. Lett. 2010, 80:1409-1413.
    • (2010) Statist. Probab. Lett. , vol.80 , pp. 1409-1413
    • Tyler, D.E.1
  • 23
    • 10044271480 scopus 로고    scopus 로고
    • A modified Weiszfeld algorithm for the Fermat-Weber location problem
    • Vardi Y., Zhang C.-H. A modified Weiszfeld algorithm for the Fermat-Weber location problem. Math. Program. 2001, 90:559-566.
    • (2001) Math. Program. , vol.90 , pp. 559-566
    • Vardi, Y.1    Zhang, C.-H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.