158
Views
105
CrossRef citations to date
0
Altmetric
Original Articles

A solution to the multivariate behrens-fisher problem

&
Pages 3719-3735 | Received 01 Jan 1986, Published online: 27 Jun 2007

References

  • Anderson , T.W. 1958 . An introduction to Multivariate Statististical Analysis , New York : John Wiley .
  • Archbold , J.W. 1958 . Algebra , London : Sir Isaac Pitman and Sons, Ltd .
  • Bellman , R. 1970 . Introduction to matrix analysis , New York : McGraw Hill .
  • Browne , M.W. 1974 . Generalized least squares estimators in the analysis of covariance structures . S. Afr. Statist. J , 8 : 1 – 24 .
  • Chikuse , Y. 1980 . Invariant polynomials with matrix arguments and their applications . Multivariate Statistical Analysis , (V) : 53 – 67 .
  • Davis , A.W. 1979 . Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory . Ann. Inst. Statist. Math , 31 : 465 – 485 . Part A
  • Davis , A.W. 1980 . Invariant polynomials with two matrix arguments extending the zonal polynomials . Multivariate Analysis , (V) : 287 – 299 . Ed. P.R. Krishnaiah
  • Davis , A.W. 1981 . On the construction of a class of invariant polynomials in several matrices, extending the zonal polynomials . Ann. Inst. Statist. Math , 33, A : 297 – 313 .
  • Davis A.W. Personal communication 1985
  • Johnson , R.A. and Wichern , D.W. Applied multivariate statistical analysis , Englewood Cliffs, N.J : Prentice Hall .
  • Nel , D.G. On the symmetric multivariate normal distribution and the asymptotic expansion of a Wishart matrix . S.A. Statist. J , 12 145 – 159 .
  • Nel , D.G. 1980 . On matrix differentiation in statistics . S. Afr. Statist. J , 14 : 137 – 193 .
  • Nel , D.G. 1981 . On patterned matrices and their applications in multivariate statistics , University of the O.F.S . Tech. Report. No. 67, Dept. of Math. Statist
  • Nel , D.G. 1985 . A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients . Linear Algebra and its Applications , 67 : 137 – 145 .
  • Pachares , J. 1955 . Note on the distribution of a definite quadratic form . Ann. Math. Statist , 26 : 128 – 131 .
  • Robbins , H. 1948 . The distribution of a definite quadratic form . Ann. Math. Statist , 19 : 266 – 270 .
  • Satterthwaite , F.E. 1946 . An aaproximate distribution of estimates of variance components . Biometrics , 2 : 110 – 114 .
  • Tan , W.Y. and Gupta , R.P. 1983 . On approximating a linear combination of central Wishart matrices with positive coefficients . Comm. Statist. Theor. Meth , 12 ( 22 ) : 2589 – 2600 .
  • Van Der Merwe , C.A. and Nel , D.G. 1985 . On the distribution of a linear sum of Wishart matrices and related matric-t variates , University of the O.F.S . Tech. Report No. 107, Dept. of Math. Statist
  • Welch , B.L. 1947 . The generalization of Student's problem when several different population variances are involved . Biometrika , 34 : 28 – 35 .
  • Wiens , D.P. 1985 . On some Pattern-Reduction matrices which appear in Statistics . Linear Algebra and its Applications , 67 : 233 – 258 .

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.