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Volumn 89, Issue 1, 2002, Pages 159-182

Spectral models for covariance matrices

Author keywords

Bartlett correction; Common principal components; Common space; Eigenprojection; Eigenspace; Elliptically contoured distribution; Maximum likelihood; Orthogonal matrix; Partial sphericity; Principal components; Proportional covariance matrices; Sphericity

Indexed keywords


EID: 3843082641     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/89.1.159     Document Type: Article
Times cited : (61)

References (57)
  • 1
    • 0001904142 scopus 로고
    • An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster
    • AIROLDI, J. P. & FLURY, B. N. (1988). An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster (Mammalia, Rodentia). J. Zool., Lond. 216, 21-36.
    • (1988) J. Zool., Lond. , vol.216 , pp. 21-36
    • Airoldi, J.P.1    Flury, B.N.2
  • 2
    • 0002815384 scopus 로고
    • Age variation in voles (Microtus californicus, M. ochrogaster) and its significance for systematic studies
    • Lawrence, KS: University of Kansas
    • AIROLDI, J. P. & HOFFMANN, R. S. (1984). Age variation in voles (Microtus californicus, M. ochrogaster) and its significance for systematic studies. In Occasional Papers of the Museum of Natural History, No. 111, pp. 1-45. Lawrence, KS: University of Kansas.
    • (1984) Occasional Papers of the Museum of Natural History , vol.111 , pp. 1-45
    • Airoldi, J.P.1    Hoffmann, R.S.2
  • 3
    • 0001699986 scopus 로고
    • Asymptotic theory for principal component analysis
    • ANDERSON, T. W. (1963). Asymptotic theory for principal component analysis. Ann. Math. Statist. 34, 122-48.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 122-148
    • Anderson, T.W.1
  • 4
    • 0032695682 scopus 로고    scopus 로고
    • Hierarchical comparison of genetic variance-covariance matrices. II. Coastal-inland divergence in the garter snake thamnophis elegans
    • ARNOLD, S. J. & PHILLIPS, P. C. (1999). Hierarchical comparison of genetic variance-covariance matrices. II. Coastal-inland divergence in the garter snake thamnophis elegans. Evolution 53, 1516-27.
    • (1999) Evolution , vol.53 , pp. 1516-1527
    • Arnold, S.J.1    Phillips, P.C.2
  • 5
    • 0030326891 scopus 로고    scopus 로고
    • Regularized Gaussian discriminant analysis through eigenvalue decomposition
    • BENSMAIL, H. & CELEUX, G. (1996). Regularized Gaussian discriminant analysis through eigenvalue decomposition. J. Am. Statist. Assoc. 91, 1743-8.
    • (1996) J. Am. Statist. Assoc. , vol.91 , pp. 1743-1748
    • Bensmail, H.1    Celeux, G.2
  • 6
    • 0038895135 scopus 로고    scopus 로고
    • Tests for linear trend in eigenvalues of a covariance matrix with application to data analysis
    • BENTLER, P. M. & YUAN, K.-H. (1996). Tests for linear trend in eigenvalues of a covariance matrix with application to data analysis. Br. J. Math. Statist. Psychol. 49, 299-312.
    • (1996) Br. J. Math. Statist. Psychol. , vol.49 , pp. 299-312
    • Bentler, P.M.1    Yuan, K.-H.2
  • 7
    • 0038492221 scopus 로고    scopus 로고
    • A local parameterization of orthogonal and semi-orthogonal matrices with applications
    • BOIK, R. J. (1998). A local parameterization of orthogonal and semi-orthogonal matrices with applications. J. Mult. Anal. 67, 244-76.
    • (1998) J. Mult. Anal. , vol.67 , pp. 244-276
    • Boik, R.J.1
  • 9
    • 0001749932 scopus 로고
    • The elimination of the unfit as illustrated by the introduced sparrow, Passer domesticus
    • 11th Lecture
    • BUMPUS, H. C. (1898). The elimination of the unfit as illustrated by the introduced sparrow, Passer domesticus. In Biological Lectures, Marine Biology Laboratory, Woods Hole, 11th Lecture, pp. 209-26.
    • (1898) Biological Lectures, Marine Biology Laboratory, Woods Hole , pp. 209-226
    • Bumpus, H.C.1
  • 10
    • 0040766419 scopus 로고
    • A remark on algorithm AS 211, the F-G algorithm
    • CLARKSON, D. B. (1988). A remark on algorithm AS 211, the F-G algorithm. Appl. Statist. 37, 147-51.
    • (1988) Appl. Statist. , vol.37 , pp. 147-151
    • Clarkson, D.B.1
  • 11
    • 38249006254 scopus 로고
    • Comparison of two factor subspaces
    • DAUXOIS, J., ROMAIN, Y. & VIGUIER, S. (1993). Comparison of two factor subspaces. J. Mult. Anal. 44, 160-78.
    • (1993) J. Mult. Anal. , vol.44 , pp. 160-178
    • Dauxois, J.1    Romain, Y.2    Viguier, S.3
  • 12
    • 0040248341 scopus 로고
    • Proportionality of covariance matrices
    • ERIKSEN, P. S. (1987). Proportionality of covariance matrices. Ann. Statist. 15, 732-48.
    • (1987) Ann. Statist. , vol.15 , pp. 732-748
    • Eriksen, P.S.1
  • 14
    • 0000643180 scopus 로고
    • Common principal components analysis
    • FLURY, B. (1984). Common principal components analysis. J. Am. Statist. Assoc. 79, 892-8.
    • (1984) J. Am. Statist. Assoc. , vol.79 , pp. 892-898
    • Flury, B.1
  • 15
    • 0345189280 scopus 로고
    • Asymptotic theory for common principal components analysis
    • FLURY, B. (1986a). Asymptotic theory for common principal components analysis. Ann. Statist. 14, 418-30.
    • (1986) Ann. Statist. , vol.14 , pp. 418-430
    • Flury, B.1
  • 16
    • 38249041581 scopus 로고
    • Proportionality of k covariance matrices
    • FLURY, B. (1986b). Proportionality of k covariance matrices. Statist. Prob. Lett. 4, 29-33.
    • (1986) Statist. Prob. Lett. , vol.4 , pp. 29-33
    • Flury, B.1
  • 17
    • 0003373430 scopus 로고
    • Two generalizations of the common principal component model
    • FLURY, B. (1987). Two generalizations of the common principal component model. Biometrika 74, 59-69.
    • (1987) Biometrika , vol.74 , pp. 59-69
    • Flury, B.1
  • 19
    • 0344727914 scopus 로고
    • Algorithm AS 211: The F-G algorithm
    • FLURY, B. & CONSTANTINE, G. (1985). Algorithm AS 211: The F-G algorithm. Appl. Statist. 34, 177-83.
    • (1985) Appl. Statist. , vol.34 , pp. 177-183
    • Flury, B.1    Constantine, G.2
  • 20
    • 0001437379 scopus 로고
    • An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form
    • FLURY, B. & GAUTSCHI, W. (1986). An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM J. Statist. Comp. 7, 169-84.
    • (1986) SIAM J. Statist. Comp. , vol.7 , pp. 169-184
    • Flury, B.1    Gautschi, W.2
  • 21
    • 21344489373 scopus 로고
    • Error rates in quadratic discrimination with constraints on the covariance matrices
    • FLURY, B., SCHMIDT, M. J. & NARAYANAN, A. (1993). Error rates in quadratic discrimination with constraints on the covariance matrices. J. Classif. 11, 101-20.
    • (1993) J. Classif. , vol.11 , pp. 101-120
    • Flury, B.1    Schmidt, M.J.2    Narayanan, A.3
  • 22
    • 21344456312 scopus 로고
    • Simultaneous detection of shift in means and variances
    • FLURY, B., NEL, D. G. & PIENAAR, I. (1995). Simultaneous detection of shift in means and variances. J. Am. Statist. Assoc. 90, 1474-81.
    • (1995) J. Am. Statist. Assoc. , vol.90 , pp. 1474-1481
    • Flury, B.1    Nel, D.G.2    Pienaar, I.3
  • 23
    • 0344295833 scopus 로고
    • An approximate test for common principal component subspaces in two groups
    • FUJIOKA, T. (1993). An approximate test for common principal component subspaces in two groups. Ann. Inst. Statist. Math. 45, 147-58.
    • (1993) Ann. Inst. Statist. Math. , vol.45 , pp. 147-158
    • Fujioka, T.1
  • 24
    • 0003831413 scopus 로고
    • New York: John Wiley & Sons
    • FULKS, W. (1978). Advanced Calculus. New York: John Wiley & Sons.
    • (1978) Advanced Calculus
    • Fulks, W.1
  • 25
    • 0040405339 scopus 로고
    • The parameterisation of orthogonal matrices: A review mainly for statisticians
    • KHURI, A. I. & GOOD, I. J. (1989). The parameterisation of orthogonal matrices: A review mainly for statisticians. S. African Statist. J. 23, 231-50.
    • (1989) S. African Statist. J. , vol.23 , pp. 231-250
    • Khuri, A.I.1    Good, I.J.2
  • 26
    • 21144468049 scopus 로고
    • Minimization of a class of matrix trace functions by means of refined majorization
    • KIERS, H. A. L. & TEN BERGE, J. M. F. (1992). Minimization of a class of matrix trace functions by means of refined majorization. Psychometrika 57, 371-82.
    • (1992) Psychometrika , vol.57 , pp. 371-382
    • Kiers, H.A.L.1    Ten Berge, J.M.F.2
  • 27
    • 0040155851 scopus 로고    scopus 로고
    • Ontogeny and individual variation: Analysis of patterned covariance matrices with common principal components
    • KLINGENBERG, C. P., NEUENSCHWANDER, B. & FLURY, B. (1996). Ontogeny and individual variation: Analysis of patterned covariance matrices with common principal components. Syst. Biol. 45, 135-50.
    • (1996) Syst. Biol. , vol.45 , pp. 135-150
    • Klingenberg, C.P.1    Neuenschwander, B.2    Flury, B.3
  • 28
    • 84950659640 scopus 로고
    • Between groups comparison of principal components
    • Corrigendum, (1981), 76, 1022
    • KRZANOWSKI, W. J. (1979). Between groups comparison of principal components. J. Am. Statist. Assoc. 74, 703-7. Corrigendum, (1981), 76, 1022.
    • (1979) J. Am. Statist. Assoc. , vol.74 , pp. 703-707
    • Krzanowski, W.J.1
  • 29
    • 0011537467 scopus 로고
    • Between-group comparison of principal components - Some sampling results
    • KRZANOWSKI, W. J. (1982). Between-group comparison of principal components - Some sampling results. J. Statist. Comp. Simul. 15, 141-54.
    • (1982) J. Statist. Comp. Simul. , vol.15 , pp. 141-154
    • Krzanowski, W.J.1
  • 30
    • 0021636260 scopus 로고
    • Principal component analysis in the presence of group structure
    • KRZANOWSKI, W. J. (1984). Principal component analysis in the presence of group structure. Appl. Statist. 33, 164-8.
    • (1984) Appl. Statist. , vol.33 , pp. 164-168
    • Krzanowski, W.J.1
  • 31
    • 0009093090 scopus 로고
    • Between-group analysis with heterogeneous covariance matrices: The common principal component model
    • KRZANOWSKI, W. J. (1990). Between-group analysis with heterogeneous covariance matrices: The common principal component model. J. Classif. 7, 81-98.
    • (1990) J. Classif. , vol.7 , pp. 81-98
    • Krzanowski, W.J.1
  • 32
    • 85012845920 scopus 로고    scopus 로고
    • The common principal components approach for clustering under multiple sampling
    • KULKARNI, B. S. & RAO, G. N. (2000). The common principal components approach for clustering under multiple sampling. J. Indian Soc. Agric. Statist. 53, 1-11.
    • (2000) J. Indian Soc. Agric. Statist. , vol.53 , pp. 1-11
    • Kulkarni, B.S.1    Rao, G.N.2
  • 33
    • 0000815369 scopus 로고
    • Tests of significance of the latent roots of covariance and correlation matrices
    • LAWLEY, D. N. (1956). Tests of significance of the latent roots of covariance and correlation matrices. Biometrika 43, 128-36.
    • (1956) Biometrika , vol.43 , pp. 128-136
    • Lawley, D.N.1
  • 34
    • 0000387723 scopus 로고
    • Matrix derivatives with an application to an adaptive linear decision problem
    • MACRAE, E. C. (1974). Matrix derivatives with an application to an adaptive linear decision problem. Ann. Statist. 2, 337-46.
    • (1974) Ann. Statist. , vol.2 , pp. 337-346
    • Macrae, E.C.1
  • 35
    • 0000489758 scopus 로고
    • The commutation matrix: Some properties and applications
    • MAGNUS, J. R. & NEUDECKER, H. (1979). The commutation matrix: some properties and applications. Ann. Statist. 7, 381-94.
    • (1979) Ann. Statist. , vol.7 , pp. 381-394
    • Magnus, J.R.1    Neudecker, H.2
  • 39
    • 0001583711 scopus 로고
    • The comparison of sample covariance matrices using likelihood ratio tests
    • MANLY, B. F. & RAYNER, J. C. W. (1987). The comparison of sample covariance matrices using likelihood ratio tests. Biometrika 74, 841-7.
    • (1987) Biometrika , vol.74 , pp. 841-847
    • Manly, B.F.1    Rayner, J.C.W.2
  • 40
    • 0004029771 scopus 로고    scopus 로고
    • Natick, MA: Mathworks, Inc.
    • MATHWORKS, INC. (1999). Matlab Version 5.3.1. Natick, MA: Mathworks, Inc.
    • (1999) Matlab Version 5.3.1
  • 42
    • 7844247931 scopus 로고    scopus 로고
    • The decomposition of the Behrens-Fisher statistic in q-dimensional common principal component submodels
    • NEL, D. G. & PIENAAR, I. (1998). The decomposition of the Behrens-Fisher statistic in q-dimensional common principal component submodels. Ann. Inst. Statist. Math. 50, 241-52.
    • (1998) Ann. Inst. Statist. Math. , vol.50 , pp. 241-252
    • Nel, D.G.1    Pienaar, I.2
  • 43
    • 0009534156 scopus 로고    scopus 로고
    • Common principal components for dependent random vectors
    • NEUENSCHWANDER, B. E. & FLURY, B. D. (2000). Common principal components for dependent random vectors. J. Mult. Anal. 75, 163-83.
    • (2000) J. Mult. Anal. , vol.75 , pp. 163-183
    • Neuenschwander, B.E.1    Flury, B.D.2
  • 44
    • 84988112998 scopus 로고
    • A neighbourhood-based classifier for LANDSAT data
    • OWEN, A. (1984). A neighbourhood-based classifier for LANDSAT data. Can. J. Statist. 12, 191-200.
    • (1984) Can. J. Statist. , vol.12 , pp. 191-200
    • Owen, A.1
  • 45
    • 0032743802 scopus 로고    scopus 로고
    • Hierarchical comparison of genetic variance-covariance matrices. I. Using the Flury hierarchy
    • PHILLIPS, P. C. & ARNOLD, S. J. (1999). Hierarchical comparison of genetic variance-covariance matrices. I. Using the Flury hierarchy. Evolution 53, 1506-15.
    • (1999) Evolution , vol.53 , pp. 1506-1515
    • Phillips, P.C.1    Arnold, S.J.2
  • 47
    • 0345158239 scopus 로고
    • Common principal component subspaces in two groups
    • SCHOTT, J. R. (1988). Common principal component subspaces in two groups. Biometrika 75, 229-36.
    • (1988) Biometrika , vol.75 , pp. 229-236
    • Schott, J.R.1
  • 48
    • 0007090002 scopus 로고
    • Some tests for common principal component subspaces in several groups
    • SCHOTT, J. R. (1991). Some tests for common principal component subspaces in several groups. Biometrika 78, 771-7.
    • (1991) Biometrika , vol.78 , pp. 771-777
    • Schott, J.R.1
  • 49
    • 0032486055 scopus 로고    scopus 로고
    • Estimating correlation matrices that have common eigenvectors
    • SCHOTT, J. R. (1998). Estimating correlation matrices that have common eigenvectors. Comp. Statist. Data Anal. 27, 445-59.
    • (1998) Comp. Statist. Data Anal. , vol.27 , pp. 445-459
    • Schott, J.R.1
  • 50
    • 0039134585 scopus 로고    scopus 로고
    • A test for proportional covariance matrices
    • SCHOTT, J. R. (1999a). A test for proportional covariance matrices. Comp. Statist. Data Anal. 32, 135-46.
    • (1999) Comp. Statist. Data Anal. , vol.32 , pp. 135-146
    • Schott, J.R.1
  • 51
    • 3843142518 scopus 로고    scopus 로고
    • Partial common principal components subspaces
    • SCHOTT, J. R. (1999b). Partial common principal components subspaces. Biometrika 86, 899-908.
    • (1999) Biometrika , vol.86 , pp. 899-908
    • Schott, J.R.1
  • 53
    • 0031714020 scopus 로고    scopus 로고
    • Using common principal components for comparing GCM Simulations
    • SENGUPTA, S. & BOYLE, J. S. (1998). Using common principal components for comparing GCM Simulations. J. Climate 11, 816-30.
    • (1998) J. Climate , vol.11 , pp. 816-830
    • Sengupta, S.1    Boyle, J.S.2
  • 54
    • 0001351797 scopus 로고
    • Analysis of covariance structures under elliptical distributions
    • SHAPIRO, A. & BROWNE, M. W. (1987). Analysis of covariance structures under elliptical distributions. J. Am. Statist. Assoc. 82, 1092-7.
    • (1987) J. Am. Statist. Assoc. , vol.82 , pp. 1092-1097
    • Shapiro, A.1    Browne, M.W.2
  • 55
    • 0001584323 scopus 로고
    • Radial estimates and the test for sphericity
    • TYLER, D. E. (1982). Radial estimates and the test for sphericity. Biometrika 69, 429-36.
    • (1982) Biometrika , vol.69 , pp. 429-436
    • Tyler, D.E.1
  • 56
    • 0001076947 scopus 로고
    • Robust and efficiency properties of scatter matrices
    • TYLER, D. E. (1983). Robust and efficiency properties of scatter matrices. Biometrika 70, 411-20.
    • (1983) Biometrika , vol.70 , pp. 411-420
    • Tyler, D.E.1
  • 57
    • 0040079600 scopus 로고
    • Test of linear trend in eigenvalues of k covariance matrices with applications in common principal components analysis
    • YUAN, K.-H. & BENTLER, P. M. (1994). Test of linear trend in eigenvalues of k covariance matrices with applications in common principal components analysis. Commun. Statist. A 23, 3141-56.
    • (1994) Commun. Statist. A , vol.23 , pp. 3141-3156
    • Yuan, K.-H.1    Bentler, P.M.2


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