메뉴 건너뛰기




Volumn 90, Issue 3, 2003, Pages 679-701

Principal component models for correlation matrices

Author keywords

Bartlett correction; Correlation matrix; Fisher scoring; Implicit function; Likelihood; Principal components analysis; Sphericity

Indexed keywords

MARTES PENNANTI;

EID: 3843053371     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/90.3.679     Document Type: Article
Times cited : (16)

References (70)
  • 1
    • 0002240143 scopus 로고
    • On the theory of multivariate elliptically contoured distributions and their applications
    • Ed. K. T. Fang and T. W. Anderson, New York: Allerton Press Inc
    • ANDERSON, T. W. & FANG, K. T. (1990). On the theory of multivariate elliptically contoured distributions and their applications. In Statistical Inferences in Elliptically Contoured and Related Distributions, Ed. K. T. Fang and T. W. Anderson, pp. 1-23. New York: Allerton Press Inc.
    • (1990) Statistical Inferences in Elliptically Contoured and Related Distributions , pp. 1-23
    • Anderson, T.W.1    Fang, K.T.2
  • 2
    • 0001615702 scopus 로고
    • On the level-error after Bartlett adjustment of the likelihood ratio statistic
    • BARNDORFF-NIELSEN, O. E. & HALL, P. (1988). On the level-error after Bartlett adjustment of the likelihood ratio statistic. Biometrika 75, 374-8.
    • (1988) Biometrika , vol.75 , pp. 374-378
    • Barndorff-Nielsen, O.E.1    Hall, P.2
  • 3
    • 84973076636 scopus 로고
    • Tests of significance in factor analysis
    • BARTLETT, M. S. (1950). Tests of significance in factor analysis. Br. J. Psychol. Statist. Sect. 3, 77-85.
    • (1950) Br. J. Psychol. Statist. Sect. , vol.3 , pp. 77-85
    • Bartlett, M.S.1
  • 4
    • 84977696515 scopus 로고
    • A further note on tests of significance in factor analysis
    • BARTLETT, M. S. (1951a). A further note on tests of significance in factor analysis. Br. J. Psychol. Statist. Sect. 4, 1-2.
    • (1951) Br. J. Psychol. Statist. Sect. , vol.4 , pp. 1-2
    • Bartlett, M.S.1
  • 5
    • 0000087757 scopus 로고
    • 2 approximation in factor analysis
    • 2 approximation in factor analysis. Biometrika 38, 337-44.
    • (1951) Biometrika , vol.38 , pp. 337-344
    • Bartlett, M.S.1
  • 6
    • 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
  • 7
    • 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
  • 8
    • 0032365923 scopus 로고    scopus 로고
    • Tests for linear trend in the smallest eigenvalues of the correlation matrix
    • BENTLER, P. M. & YUAN, K-H. (1998). Tests for linear trend in the smallest eigenvalues of the correlation matrix. Psychometrika 63, 131-44.
    • (1998) Psychometrika , vol.63 , pp. 131-144
    • Bentler, P.M.1    Yuan, K.-H.2
  • 9
    • 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
  • 10
    • 3843082641 scopus 로고    scopus 로고
    • Spectral models for covariance matrices
    • BOIK, R. J. (2002). Spectral models for covariance matrices. Biometrika 89, 159-82.
    • (2002) Biometrika , vol.89 , pp. 159-182
    • Boik, R.J.1
  • 11
    • 0001963735 scopus 로고
    • Generalized least squares estimators in the analysis of covariance structures
    • BROWNE, M. W. (1974). Generalized least squares estimators in the analysis of covariance structures. S. African Statist. J. 8, 1-24.
    • (1974) S. African Statist. J. , vol.8 , pp. 1-24
    • Browne, M.W.1
  • 12
    • 0002490751 scopus 로고
    • Covariance structures
    • Ed. D. M. Hawkins, Cambridge, U.K.: Cambridge University Press
    • BROWNE, M. W. (1982). Covariance structures. In Topics in Applied Multivariate Analysis, Ed. D. M. Hawkins, pp. 72-141. Cambridge, U.K.: Cambridge University Press.
    • (1982) Topics in Applied Multivariate Analysis , pp. 72-141
    • Browne, M.W.1
  • 13
    • 85004870441 scopus 로고
    • Asymptotically distribution-free methods for the analysis of covariance structures
    • BROWNE, M. W. (1984), Asymptotically distribution-free methods for the analysis of covariance structures, Br. J. Math. Statist. Psychol. 37, 62-83.
    • (1984) Br. J. Math. Statist. Psychol. , vol.37 , pp. 62-83
    • Browne, M.W.1
  • 14
    • 38249039339 scopus 로고
    • The asymptotic covariance matrix of sample correlation coefficients under general conditions
    • BROWNE, M. W. & SHAPIRO, A. (1986). The asymptotic covariance matrix of sample correlation coefficients under general conditions. Lin. Algeb. Applic. 82, 169-76.
    • (1986) Lin. Algeb. Applic. , vol.82 , pp. 169-176
    • Browne, M.W.1    Shapiro, A.2
  • 15
    • 0009659160 scopus 로고    scopus 로고
    • Comparisons of multivariate relational structures in serially correlated data
    • COHN, R. (1999). Comparisons of multivariate relational structures in serially correlated data. J. Agric. Biol. Envir. Statist. 4, 238-57.
    • (1999) J. Agric. Biol. Envir. Statist. , vol.4 , pp. 238-257
    • Cohn, R.1
  • 16
    • 0000534626 scopus 로고
    • Analysis of correlation matrices using covariance structure models
    • CUDECK, R. (1989). Analysis of correlation matrices using covariance structure models. Psychol. Bull. 105, 317-27.
    • (1989) Psychol. Bull. , vol.105 , pp. 317-327
    • Cudeck, R.1
  • 17
    • 0001008882 scopus 로고
    • 2 random variables (Algorithm AS 155)
    • 2 random variables (Algorithm AS 155). Appl. Statist. 29, 323-33.
    • (1980) Appl. Statist. , vol.29 , pp. 323-333
    • Davies, R.B.1
  • 18
    • 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
  • 20
    • 21144465864 scopus 로고
    • Tail areas of linear combinations of chi-squares and non-central chi-squares
    • FIELD, C. (1993). Tail areas of linear combinations of chi-squares and non-central chi-squares. J. Statist. Comp. Simul. 45, 243-8.
    • (1993) J. Statist. Comp. Simul. , vol.45 , pp. 243-248
    • Field, C.1
  • 21
    • 3843084806 scopus 로고
    • The simultaneous distribution of correlation coefficients
    • FISHER, R. A. (1962). The simultaneous distribution of correlation coefficients. Sankhyā A 24, 1-8.
    • (1962) Sankhyā A , vol.24 , pp. 1-8
    • Fisher, R.A.1
  • 22
    • 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
  • 23
    • 0345189280 scopus 로고
    • Asymptotic theory for common principal components analysis
    • FLURY, B. (1986). Asymptotic theory for common principal components analysis. Ann. Statist. 14, 418-30.
    • (1986) Ann. Statist. , vol.14 , pp. 418-430
    • Flury, B.1
  • 24
    • 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
  • 26
  • 27
    • 0000793351 scopus 로고
    • On the sampling theory of roots of determinantal equations
    • GIRSHICK, M. A. (1939). On the sampling theory of roots of determinantal equations. Ann. Math. Statist. 10, 203-24.
    • (1939) Ann. Math. Statist. , vol.10 , pp. 203-224
    • Girshick, M.A.1
  • 28
    • 0000070968 scopus 로고
    • On the removal of skewness by transformation
    • HALL, P. (1992). On the removal of skewness by transformation. J. R. Statist. Soc. B 54, 221-8.
    • (1992) J. R. Statist. Soc. B , vol.54 , pp. 221-228
    • Hall, P.1
  • 30
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • HOTELLING, H. (1933). Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24, 417-41, 498-520.
    • (1933) J. Educ. Psychol. , vol.24 , pp. 417-441
    • Hotelling, H.1
  • 31
    • 3843081579 scopus 로고
    • The limiting distribution of functions of sample means and applications to testing hypotheses
    • Ed. J. Neyman, Berkeley: University of California Press
    • HSU, P. L. (1949). The limiting distribution of functions of sample means and applications to testing hypotheses. In Proc. Berkeley Symp. Math. Statist. Prob., Ed. J. Neyman, pp. 359-402. Berkeley: University of California Press.
    • (1949) Proc. Berkeley Symp. Math. Statist. Prob. , pp. 359-402
    • Hsu, P.L.1
  • 32
    • 3843064274 scopus 로고
    • Asymptotic distributions of eigenprojectors of covariance and correlation matrices for testing hypotheses
    • KOLLO, T. (1984). Asymptotic distributions of eigenprojectors of covariance and correlation matrices for testing hypotheses. Acta Comment. Univ. Tartuensis 685, 3-13.
    • (1984) Acta Comment. Univ. Tartuensis , vol.685 , pp. 3-13
    • Kollo, T.1
  • 33
    • 3843092505 scopus 로고    scopus 로고
    • Asymptotic inference based on eigenprojections of covariance and correlation matrices
    • Ed. R. J. Heijmans, D. S. G. Pollock and A. Satorra, Dordrecht: Kluwer Academic Publishers
    • KOLLO, T. (1999). Asymptotic inference based on eigenprojections of covariance and correlation matrices. In Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker, Ed. R. J. Heijmans, D. S. G. Pollock and A. Satorra, pp. 207-22. Dordrecht: Kluwer Academic Publishers.
    • (1999) Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker , pp. 207-222
    • Kollo, T.1
  • 34
    • 0000542317 scopus 로고
    • Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices
    • KOLLO, T. & NEUDECKER, H. (1993). Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices. J. Mult. Anal. 47, 283-300. Corrigendum (1994) 51, 210.
    • (1993) J. Mult. Anal. , vol.47 , pp. 283-300
    • Kollo, T.1    Neudecker, H.2
  • 35
    • 0000542317 scopus 로고
    • KOLLO, T. & NEUDECKER, H. (1993). Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices. J. Mult. Anal. 47, 283-300. Corrigendum (1994) 51, 210.
    • (1994) Corrigendum , vol.51 , pp. 210
  • 36
    • 0010005682 scopus 로고    scopus 로고
    • Asymptotics of Pearson-Hotelling principal component vectors of sample variance and correlation matrices
    • KOLLO, T. & NEUDECKER, H. (1997). Asymptotics of Pearson-Hotelling principal component vectors of sample variance and correlation matrices. Behaviormetrika 24, 51-69.
    • (1997) Behaviormetrika , vol.24 , pp. 51-69
    • Kollo, T.1    Neudecker, H.2
  • 37
    • 0009129990 scopus 로고
    • Unbiased estimation of fourth-order matrix moments
    • KONING, H., NEUDECKER, H. & WANSBEEK, T. (1992). Unbiased estimation of fourth-order matrix moments. Lin. Algeb. Applic. 160, 163-74.
    • (1992) Lin. Algeb. Applic. , vol.160 , pp. 163-174
    • Koning, H.1    Neudecker, H.2    Wansbeek, T.3
  • 38
    • 84984277047 scopus 로고
    • Asymptotic expansions for the distributions of statistics based on a correlation matrix
    • KONISHI, S. (1978). Asymptotic expansions for the distributions of statistics based on a correlation matrix. Can. J. Statist. 6, 49-56.
    • (1978) Can. J. Statist. , vol.6 , pp. 49-56
    • Konishi, S.1
  • 39
    • 0000815369 scopus 로고
    • Tests of significance for the latent roots of covariance and correlation matrices
    • LAWLEY, D. N. (1956). Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43, 128-36.
    • (1956) Biometrika , vol.43 , pp. 128-136
    • Lawley, D.N.1
  • 40
    • 1542412267 scopus 로고
    • On testing a set of correlation coefficients for equality
    • LAWLEY, D. N. (1963). On testing a set of correlation coefficients for equality. Ann. Math. Statist. 34, 149-51.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 149-151
    • Lawley, D.N.1
  • 41
    • 0039013352 scopus 로고
    • Algorithm AS 213. Generation of population correlation matrices with specified eigenvalues
    • LIN, S. P. & BENDEL, R. B. (1985). Algorithm AS 213. Generation of population correlation matrices with specified eigenvalues. Appl. Statist. 34, 193-8.
    • (1985) Appl. Statist. , vol.34 , pp. 193-198
    • Lin, S.P.1    Bendel, R.B.2
  • 42
    • 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
  • 43
    • 0004237651 scopus 로고
    • London: Charles Friggin & Company Ltd.
    • MAGNUS, J. R. (1988). Linear Structures. London: Charles Friggin & Company Ltd.
    • (1988) Linear Structures
    • Magnus, J.R.1
  • 44
    • 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. 1, 381-94.
    • (1979) Ann. Statist. , vol.1 , pp. 381-394
    • Magnus, J.R.1    Neudecker, H.2
  • 47
    • 0000766187 scopus 로고
    • A first study of the Tibetan skull
    • MORANT, G. M. (1923). A first study of the Tibetan skull. Biometrika 14, 193-260.
    • (1923) Biometrika , vol.14 , pp. 193-260
    • Morant, G.M.1
  • 48
    • 0002330292 scopus 로고
    • A matrix derivation of the asymptotic covariance matrix of correlation coefficients
    • NELL, D. G. (1985). A matrix derivation of the asymptotic covariance matrix of correlation coefficients. Lin. Algeb. Applic. 67, 137-45.
    • (1985) Lin. Algeb. Applic. , vol.67 , pp. 137-145
    • Nell, D.G.1
  • 49
    • 21344447903 scopus 로고    scopus 로고
    • The asymptotic variance matrices of the sample correlation matrix in elliptical and normal situations and their proportionality
    • NEUDECKER, H. (1996). The asymptotic variance matrices of the sample correlation matrix in elliptical and normal situations and their proportionality. Lin. Algeb. Applic. 237/238, 127-32.
    • (1996) Lin. Algeb. Applic. , vol.237-238 , pp. 127-132
    • Neudecker, H.1
  • 50
    • 38249020616 scopus 로고
    • The asymptotic variance matrix of the sample correlation matrix
    • NEUDECKER, H. & WESSELMAN, A. M. (1990). The asymptotic variance matrix of the sample correlation matrix. Lin. Algeb. Applic. 127, 589-99.
    • (1990) Lin. Algeb. Applic. , vol.127 , pp. 589-599
    • Neudecker, H.1    Wesselman, A.M.2
  • 51
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • PEARSON, K. (1901). On lines and planes of closest fit to systems of points in space. Phil. Mag. 2, 559-72.
    • (1901) Phil. Mag. , vol.2 , pp. 559-572
    • Pearson, K.1
  • 52
    • 0000159074 scopus 로고
    • Mathematical contributions to the theory of evolution. IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlation
    • PEARSON, K. & FILON, L. N. G. (1898). Mathematical contributions to the theory of evolution. IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlation. Phil. Trans. R. Soc. Land. A 191, 229-311.
    • (1898) Phil. Trans. R. Soc. Land. A , vol.191 , pp. 229-311
    • Pearson, K.1    Filon, L.N.G.2
  • 53
    • 0345158239 scopus 로고
    • Common principal component subspaces in two groups
    • SCHOTT, J. R. (1988a). Common principal component subspaces in two groups. Biometrika 75, 229-36.
    • (1988) Biometrika , vol.75 , pp. 229-236
    • Schott, J.R.1
  • 54
    • 0042904981 scopus 로고
    • Testing the equality of the smallest latent roots of a correlation matrix
    • SCHOTT, J. R. (1988b). Testing the equality of the smallest latent roots of a correlation matrix. Biometrika 75, 794-6.
    • (1988) Biometrika , vol.75 , pp. 794-796
    • Schott, J.R.1
  • 55
    • 0040999451 scopus 로고
    • A test for a specific principal component of a correlation matrix
    • SCHOTT, J. R. (1991a). A test for a specific principal component of a correlation matrix. J. Am. Statist. Assoc. 86, 747-51.
    • (1991) J. Am. Statist. Assoc. , vol.86 , pp. 747-751
    • Schott, J.R.1
  • 56
    • 0007090002 scopus 로고
    • Some tests for common principal component subspaces in several groups
    • SCHOTT, J. R. (1991b). 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
  • 57
    • 0042037856 scopus 로고    scopus 로고
    • Eigenprojections and the equality of latent roots of a correlation matrix
    • SCHOTT, J. R. (1996). Eigenprojections and the equality of latent roots of a correlation matrix. Comp. Statist. Data Anal. 23, 229-38.
    • (1996) Comp. Statist. Data Anal. , vol.23 , pp. 229-238
    • Schott, J.R.1
  • 58
    • 0007038401 scopus 로고    scopus 로고
    • Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis
    • SCHOTT, J. R. (1997). Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis. Biometrika 84, 327-37.
    • (1997) Biometrika , vol.84 , pp. 327-337
    • Schott, J.R.1
  • 59
    • 0032486055 scopus 로고    scopus 로고
    • Estimating correlation matrices that have common eigenvectors
    • SCHOTT, J. R. (1998a). 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
  • 60
    • 3843088175 scopus 로고    scopus 로고
    • Inferences relating to the multiplicity of the smallest eigenvalue of a correlation matrix
    • SCHOTT, J. R. (1998b). Inferences relating to the multiplicity of the smallest eigenvalue of a correlation matrix. Sankhyā B 60, 215-20.
    • (1998) Sankhyā B , vol.60 , pp. 215-220
    • Schott, J.R.1
  • 61
    • 0039134585 scopus 로고    scopus 로고
    • A test for proportional covariances
    • SCHOTT, J. R. (1999). A test for proportional covariances. Comp. Statist. Data Anal. 32, 135-46.
    • (1999) Comp. Statist. Data Anal. , vol.32 , pp. 135-146
    • Schott, J.R.1
  • 63
    • 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
  • 64
    • 38249020046 scopus 로고
    • On the treatment of correlation structures as covariance structures
    • SHAPIRO, A. & BROWNE, M. W. (1990). On the treatment of correlation structures as covariance structures. Lin. Algeb. Applic. 127, 567-87.
    • (1990) Lin. Algeb. Applic. , vol.127 , pp. 567-587
    • Shapiro, A.1    Browne, M.W.2
  • 65
    • 0011425031 scopus 로고    scopus 로고
    • On asymptotics of estimating functions
    • SØRENSEN, M. (1999). On asymptotics of estimating functions. Brazilian J. Prob. Statist. 13, 111-36.
    • (1999) Brazilian J. Prob. Statist. , vol.13 , pp. 111-136
    • Sørensen, M.1
  • 66
    • 85004899657 scopus 로고
    • The asymptotic distribution of the elements of a correlation matrix: Theory and application
    • STEIGER, J. H. & HAKSTIAN, A. R. (1982). The asymptotic distribution of the elements of a correlation matrix: Theory and application. Br. J. Math. Statist. Psychol. 35, 208-15.
    • (1982) Br. J. Math. Statist. Psychol. , vol.35 , pp. 208-215
    • Steiger, J.H.1    Hakstian, A.R.2
  • 67
    • 85004788425 scopus 로고
    • A historical note on the asymptotic distribution of correlations
    • STEIGER, J. H. & HAKSTIAN, A. R. (1983). A historical note on the asymptotic distribution of correlations. Br. J. Math. Statist. Psychol. 36, 157.
    • (1983) Br. J. Math. Statist. Psychol. , vol.36 , pp. 157
    • Steiger, J.H.1    Hakstian, A.R.2
  • 68
    • 2442447448 scopus 로고
    • On the multivariate asymptotic distribution of sequential chi-square statistics
    • STEIGER, J. H., SHAPIRO, A. & BROWNE, M. W. (1985). On the multivariate asymptotic distribution of sequential chi-square statistics. Psychometrika 50, 253-64.
    • (1985) Psychometrika , vol.50 , pp. 253-264
    • Steiger, J.H.1    Shapiro, A.2    Browne, M.W.3
  • 69
    • 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
  • 70
    • 0001040805 scopus 로고    scopus 로고
    • Asymptotics of estimating equations under natural conditions
    • YUAN, K.-H. & JENNRICH, R. I. (1998). Asymptotics of estimating equations under natural conditions. J. Mult. Anal. 65, 245-60.
    • (1998) J. Mult. Anal. , vol.65 , pp. 245-260
    • Yuan, K.-H.1    Jennrich, R.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.