111
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Construction, properties and statistical applications of positive definite intraclass matrix

Pages 891-904 | Received 29 Apr 2010, Accepted 07 Oct 2010, Published online: 14 Apr 2011

References

  • Aitkin , MA , Nelson , WC and Reinfort , KH . 1968 . Tests for correlation matrices . Biometrika , 55 : 327 – 334 .
  • Bellman , R . 1974 . Introduction to Matrix Analysis, , 2nd , New Delhi : Tata McGraw-Hill .
  • Brockwell , PJ and Davis , RA . 2002 . Introduction to Time Series & Forecasting, , 2nd , New York : Springer .
  • Cronbach , LJ . 1951 . Coefficient alpha and the internal structure of tests . Psychometrika , 16 : 297 – 334 .
  • Eaton , ML and Perlman , MD . 1973 . The non singularity of generalized sample covariance matrices . Ann. Stat. , 1 : 710 – 717 .
  • Geisser , S . 1963 . Multivariate analysis of variance for a special case . J. Am. Stat. Assoc. , 58 : 660 – 669 .
  • Goodman , M . 1968 . A measure of ‘overall variability’ in populations . Biometrics , 24 : 189 – 192 .
  • Graybill , FA . 1969 . Introduction to Matrices with Applications in Statistics , Belmont, CA : Wadsworth .
  • Gulliksen , H . 1950 . Theory of Mental Tests , New York : John Wiley .
  • Johnson , CR , Kumar , R and Wolkowicz , H . 1985 . Lower bounds for the spread of a matrix . Linear Algebra Appl. , 71 : 161 – 173 .
  • Jolicoeur , P and Mosimann , JE . 1960 . Size and shape variation in the painted turtle: A principal component analysis . Growth , 24 : 339 – 354 .
  • Kshirsagar , AM . 1983 . A Course in Linear Models , New York : Marcel Dekker .
  • Marcus , M and Minc , H . 1964 . A Survey of Matrix Theory & Matrix Inequalities , New York : Dover Publications .
  • Morrison , DF . 1978 . Multivariate Statistical Methods, , 2nd , New York : McGrawHill .
  • Mukherjee , BN . 1970 . Likelihood ratio tests of statistical hypotheses associated with patterned covariance matrices in Psychology . Brit. J. Math. Stat. Psychol. , 23 : 89 – 120 .
  • Mukherjee , BN . 1976 . Techniques of covariance structural analysis . Aust. J. Stat. , 18 : 131 – 150 .
  • B.N. Mukherjee, A Simple Approach to Testing of Hypothesis Regarding a Class of Covariance Structures, Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions, Calcutta, 1981, pp. 171–192
  • Mukherjee , BN and Maiti , SS . 1988 . On conditions for equality of OLSE, GLSE and MLE in analysis of covariance structures . Calcutta Stat. Assoc. Bull. , 37 : 171 – 192 .
  • Rao , CR . 2002 . Linear Statistical Inference and its Applications, , 2nd , Singapore : John Wiley .
  • Rogers , GS and Young , DL . 1977 . Explicit maximum likelihood estimators for certain patterned covariance matrices . Commun. Stat. Theory Methods , A6 : 121 – 133 .
  • Sokal , RR . 1965 . Statistical methods in systematics . Bio. Rev. Camb. Phil. Soc. , 40 : 337 – 391 .
  • Takeuchi , K , Yanai , H and Mukherjee , BN . 1982 . The Foundations of the Multivariate Analysis , New Delhi : Wiley Eastern .
  • Wilks , SS . 1946 . Sample Criteria for testing means, equality of variance and equality of covariance in a normal multivariate distribution . Ann. Math. Stat. , 17 : 257 – 281 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.