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Original Articles

ML estimation for the multivariate normal distribution with general linear model mea1 and linear-structure covariance matrix; one-population, complete-data case

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Pages 1927-1955 | Published online: 27 Jun 2007

References

  • Anderson , T.W. 1969 . Statistical inference for covariance matrices with linear structure . Proceedings of the Second International Symposium on Multivariate Analysis , : 55 – 66 .
  • Anderson , T.W. 1970 . Estimation of covariance matrices which are linear combinations of given matrices . Essays in Probability and Statistics , : 1 – 24 .
  • Anderson , T.W. 1973 . Asymptotic efficient estimation of covariance matrices with linear structure . Ann.Statist. , 1 : 135 – 141 .
  • Andrade , D.F. and Helms , R.W. 1984 . Maximum likelihood estimates in the multivariate normal with patterned mean and covariance via the EM algorithm . Commun.Statist.Theor.Meth. , 13 : 2239 – 2251 .
  • Bishop , Y.M.M. , Fienberg , S.E. and Holland , P.W. 1975 . Discrete Multivariate Analysis: Theory and Practice , Cambridge : MIT Press .
  • Cole and James , W.L. 1969 . Multivariate analysis of variance . Institute of Statistics Mimeo Series No. 640 ,
  • Dempster , A.P. , Laird , N.M. and Rubin , D.B. 1977 . Maximum likelihood from incomplete data via the EM algorithm . J.R.S.S. , B 39 : 1 – 38 .
  • Laird , N.M. 1982 . Computation of variance components using the EM algorithm . J.Statist.Comput.Simul. , 14 : 295 – 303 .
  • Olkin , I. 1972 . Testing and estimation for structures which are circulary symmetric in blocks . Proceedings of the Symposium on Multivariate Analysis , 14 : 183 – 195 .
  • Olkin , I. and Prss , S.J. 1969 . Testing and estimation for a circular stationary model . Ann.Math.Statist. , 40 : 1358 – 1373 .
  • Rao , C.R. 1973 . Linear Statistical Inference and Its Application , New York : Wiley .
  • Rogers , G.S. and Young , D.L. 1975 . Some likelihood ratio tests when a normal covariance matrix has certain reducible linear structures . Comm.Statist. , 4 : 537 – 554 .
  • Rogers , G.S. and Young , D.L. 1977 . Explicit maximum likelihood estimators for certain patterned covariance matrices . Commum.Statist. , A6 : 121 – 133 .
  • Rogers , G.S. and Young , D.L. 1978 . On testing a multivariate linear hypothesis when the covariance matrix and its inverse have the same pattern . J.A.S.A. , 73 : 203 – 207 .
  • Szatrowski , T.H. 1979 . Asymptotic nonnull distributions in the multivariate normal patterned mean and covariance matrix testing problem . Ann.Statist. , 7 : 823 – 837 .
  • Szatrowski , T.H. 1980 . Necessary and sufficient conditions for explicit solutions in the multivariate normal estimation problem for patterned means and covariances . Ann.Statist. , 8 : 802 – 810 .
  • Szatrowski , T.H. 1981 . Missing data in the multivariate normal patterned mean and covariance matrix testing and estimation problem , 81 – 17 . New Jersey : Princeton .
  • Szatrowski , T.H. 1983 . Mising data in one-population multivariate normal patterned mean and covariance matrix testing and estimation problem . Ann.Statist. , 11 : 947 – 958 .
  • Szatrowski , T.H. and Miller , J.J. 1980 . Explicit maximum likelihood estimates from balanced data in the mixed model of the analysis of variance . Ann.Statist. , 8 : 811 – 819 .
  • Votaw , D.F. 1948 . Testing compound symmetry in a normal multivariate distribution . Ann.Math.Statist. , 19 : 447 – 473 .
  • Wilks , S.S. 1946 . Sample criteria for testing equality of means, equality of variances and equality of covariances in a normal multivavariate distribution . Ann.Math.Statist. , 17 : 257 – 281 .
  • Young , D.L. 1976 . Inference conccerning the mean vector when the covariance matrix is totally reducible . J.A.S.A. , 71 : 696 – 699 .

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