메뉴 건너뛰기




Volumn 64, Issue 2, 1999, Pages 105-123

The MLE algorithm for the matrix normal distribution

Author keywords

Existence and stability of estimators; Matrix normal distribution; Maximum likelihood estimation; Separability of variance covariance structure; Test of model adequacy; Two stage algorithm

Indexed keywords


EID: 0033236298     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659908811970     Document Type: Article
Times cited : (248)

References (35)
  • 2
    • 0002972259 scopus 로고
    • Methods for assessing multivariate normality
    • Krishnaiah, P. R. (Ed.), Academic Press, New York
    • Andrews, D. F., Gnanadesikan, R. and Warner, J. L. (1973) Methods for assessing multivariate normality. In: Multivariate Analysis III, Krishnaiah, P. R. (Ed.), Academic Press, New York, pp. 95-116.
    • (1973) Multivariate Analysis III , pp. 95-116
    • Andrews, D.F.1    Gnanadesikan, R.2    Warner, J.L.3
  • 4
    • 0000695172 scopus 로고
    • The mixed model for multivariate repeated measures: Validity conditions and an approximate test
    • Boik, R. J. (1988) The mixed model for multivariate repeated measures: validity conditions and an approximate test. Psychometrika, 53, 469-486.
    • (1988) Psychometrika , vol.53 , pp. 469-486
    • Boik, R.J.1
  • 5
    • 0000235653 scopus 로고
    • Some theorems on quadratic forms applied in the study of analysis of variance problems. I. Effect of inequality of variance in the one-way classification
    • Box, G. E. P. (1954a) Some theorems on quadratic forms applied in the study of analysis of variance problems. I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics, 25, 290-302.
    • (1954) Annals of Mathematical Statistics , vol.25 , pp. 290-302
    • Box, G.E.P.1
  • 6
    • 0000235654 scopus 로고
    • Some theorems on quadratic forms applied in the study of analysis of variance problems. II. Effects of inequality of variance and of correlation between errors in the two-way classification
    • Box, G. E. P. (1954b) Some theorems on quadratic forms applied in the study of analysis of variance problems. II. Effects of inequality of variance and of correlation between errors in the two-way classification. Annals of Mathematical Statistics, 25, 484-498.
    • (1954) Annals of Mathematical Statistics , vol.25 , pp. 484-498
    • Box, G.E.P.1
  • 9
    • 0000043041 scopus 로고
    • Some matrix-variate distribution theory: Notational considerations and a Bayesian application
    • Dawid, A. P. (1981) Some matrix-variate distribution theory: notational considerations and a Bayesian application. Biometrika, 68, 265-274.
    • (1981) Biometrika , vol.68 , pp. 265-274
    • Dawid, A.P.1
  • 10
    • 0009104337 scopus 로고
    • Matrix-valued distributions
    • Kotz, S. and Johnson, N. L. (Eds.), Wiley, New York
    • de Waal, D. J. (1988) Matrix-valued distributions. In: Encyclopedia of Statistical Sciences, 5, Kotz, S. and Johnson, N. L. (Eds.), Wiley, New York, pp. 326-333.
    • (1988) Encyclopedia of Statistical Sciences , vol.5 , pp. 326-333
    • De Waal, D.J.1
  • 11
    • 0009105777 scopus 로고
    • Standard error evaluation in grid sampling: Interest of the matrix normal distribution
    • Namur, Belgium, July 18-22
    • Delincé, J., Gérard, G. and Byakagaba, M. (1988) Standard error evaluation in grid sampling: interest of the matrix normal distribution, Abstract. Proceedings of The XIVth International Biometric Conference, Namur, Belgium, July 18-22, p. 32.
    • (1988) Proceedings of the XIVth International Biometric Conference , pp. 32
    • Delincé, J.1    Gérard, G.2    Byakagaba, M.3
  • 13
    • 0027286249 scopus 로고
    • Modifying the t-test for assessing the correlation between two spatial processes
    • Dutilleul, P. (1993) Modifying the t-test for assessing the correlation between two spatial processes. Biometrics, 49, 305-314.
    • (1993) Biometrics , vol.49 , pp. 305-314
    • Dutilleul, P.1
  • 14
    • 0030440716 scopus 로고    scopus 로고
    • A doubly multivariate model for statistical analysis of spatio-temporal environmental data
    • Dutilleul, P. and Pinel-Alloul, B. (1996) A doubly multivariate model for statistical analysis of spatio-temporal environmental data. Environmetrics, 7, 551-566.
    • (1996) Environmetrics , vol.7 , pp. 551-566
    • Dutilleul, P.1    Pinel-Alloul, B.2
  • 15
    • 0002882051 scopus 로고    scopus 로고
    • Incorporating scale in ecological experiments: Data analysis
    • Peterson, D. L. and Parker, V. T. (Eds.), Columbia University Press, New York
    • Dutilleul, P. (1998) Incorporating scale in ecological experiments: Data analysis. In: Ecological Scale: Theory and Applications, Peterson, D. L. and Parker, V. T. (Eds.), Columbia University Press, New York, pp. 387-425.
    • (1998) Ecological Scale: Theory and Applications , pp. 387-425
    • Dutilleul, P.1
  • 16
    • 0000115992 scopus 로고
    • Some applications of matrix derivates in multivariate analysis
    • Dwyer, P. S. (1967) Some applications of matrix derivates in multivariate analysis. Journal of the American Statistical Association, 62, 607-625.
    • (1967) Journal of the American Statistical Association , vol.62 , pp. 607-625
    • Dwyer, P.S.1
  • 19
    • 84950658629 scopus 로고
    • Conditions under which mean square ratios in repeated measurements designs have exact F-distributions
    • Huynh, H. and Feldt, L. S. (1970) Conditions under which mean square ratios in repeated measurements designs have exact F-distributions. Journal of the American Statistical Association, 65, 1582-1589.
    • (1970) Journal of the American Statistical Association , vol.65 , pp. 1582-1589
    • Huynh, H.1    Feldt, L.S.2
  • 21
    • 38249040778 scopus 로고
    • The distribution of a generalized least squares estimator with covariance adjustment
    • Kenward, M. G. (1986) The distribution of a generalized least squares estimator with covariance adjustment. Journal of Multivariate Analysis, 20, 244-250.
    • (1986) Journal of Multivariate Analysis , vol.20 , pp. 244-250
    • Kenward, M.G.1
  • 23
    • 0000904196 scopus 로고
    • Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies
    • Mardia, K. V. (1974) Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankhyā Series B, 36, 115-128.
    • (1974) Sankhyā Series B , vol.36 , pp. 115-128
    • Mardia, K.V.1
  • 25
    • 70350340104 scopus 로고
    • Test for univariate and multivariate normality
    • Krishnaiah, P. R. (Ed.), North-Holland, Amsterdam
    • Mardia, K. V. (1980) Test for univariate and multivariate normality. In: Handbook of Statistics, 1, Krishnaiah, P. R. (Ed.). North-Holland, Amsterdam, pp. 279-320.
    • (1980) Handbook of Statistics , vol.1 , pp. 279-320
    • Mardia, K.V.1
  • 27
    • 0009247315 scopus 로고
    • On patterned matrix normal distributions
    • University of the Orange Free State, Bloemfontein, South Africa
    • Nel, D. G. (1979) On patterned matrix normal distributions. Mathematical Statistics Department Technical Report. 48, University of the Orange Free State, Bloemfontein, South Africa.
    • (1979) Mathematical Statistics Department Technical Report , vol.48
    • Nel, D.G.1
  • 28
    • 0009179370 scopus 로고
    • On distributions and moments associated with matrix normal distributions
    • University of the Orange Free State, Bloemfontein, South Africa
    • Nel, H. M. (1977) On distributions and moments associated with matrix normal distributions. Mathematical Statistics Department Technical Report, 24, University of the Orange Free State, Bloemfontein, South Africa.
    • (1977) Mathematical Statistics Department Technical Report , vol.24
    • Nel, H.M.1
  • 29
    • 0000661332 scopus 로고
    • A generalized multivariate analysis of variance model useful especially for growth curve problems
    • Potthoff, R. F. and Roy, S. N. (1964) A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313-326.
    • (1964) Biometrika , vol.51 , pp. 313-326
    • Potthoff, R.F.1    Roy, S.N.2
  • 30
    • 0001940268 scopus 로고
    • Covariance adjustment and related problems in multivariate analysis
    • Krishnaiah, P. R. (Ed.), Academic Press, New York
    • Rao, C. R. (1966) Covariance adjustment and related problems in multivariate analysis. In: Multivariate Analysis, Krishnaiah, P. R. (Ed.), Academic Press, New York, pp. 87-103.
    • (1966) Multivariate Analysis , pp. 87-103
    • Rao, C.R.1
  • 31
    • 0000737837 scopus 로고
    • Multivariate repeated-measurement or growth curve models with multivariate random-effects covariance structure
    • Reinsel, G. (1982) Multivariate repeated-measurement or growth curve models with multivariate random-effects covariance structure. Journal of the American Statistical Association, 77, 190-195.
    • (1982) Journal of the American Statistical Association , vol.77 , pp. 190-195
    • Reinsel, G.1
  • 34
    • 0009247316 scopus 로고
    • Univariate repeated measures techniques applied to multivariate data
    • Thomas, D. R. (1983) Univariate repeated measures techniques applied to multivariate data. Psychometrika, 48, 451-464.
    • (1983) Psychometrika , vol.48 , pp. 451-464
    • Thomas, D.R.1
  • 35
    • 70350346915 scopus 로고
    • Multivariate analysis of variance of repeated measurements
    • Krishnaiah, P. R. (Ed.), North-Holland, Amsterdam
    • Timm, N. H. (1980) Multivariate analysis of variance of repeated measurements. In: Handbook of Statistics. 1, Krishnaiah, P. R. (Ed.), North-Holland, Amsterdam, pp. 41-87.
    • (1980) Handbook of Statistics , vol.1 , pp. 41-87
    • Timm, N.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.