The heteroscedastic method: Multivariate implementation

  • Edward J. Dudewicz
  • Vidya S. Taneja


Over the past decade, procedures have been developed which allow one (in the univariate case) to make inferences about means even in the presence of unknown and unequal variances. A general method (called The Heteroscedastic Method) allowing this in all statistical problems simultaneously was formulated in 1979 and allowed specifically for the multivariate case (e.g., MANOVA and other multivariate inferences). While in the univariate case The Heteroscedastic Method is readily implemented, in the multivariate case practical implementation was not heretofore possible since a certain problem in construction of matrices required by the method had not been solved. In this paper we solve that problem and give a computer algorithm allowing for use of the solution in The Heteroscedastic Method.

Key words and phrases

Heteroscedasticity multivariate analysis heteroscedastic inference matrices 


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  1. [1]
    Chapman, D. G. (1950). Some two sample tests,Ann. Math. Statist.,21, 601–606.MathSciNetMATHGoogle Scholar
  2. [2]
    Chatterjee, S. K. (1959). On an extension of Stein's two-sample procedure to the multi-normal problem,Calcutta Statist. Ass. Bull.,8, 121–148.MathSciNetMATHGoogle Scholar
  3. [3]
    Dudewicz, E. J. (1983). Heteroscedasticity,Encyclopedia of Statistical Sciences (eds. N. L. Johnson, S. Kotz and C. B. Read), John Wiley and Sons, Inc., New York,3, 611–619.Google Scholar
  4. [4]
    Dudewicz, E. J. and Bishop, T. A. (1979). The heteroscedastic method,Optim. Meth. Statist. (ed. J. S. Rustagi), Academic Press, New York, 183–203.Google Scholar
  5. [5]
    Dudewicz, E. J. and Dalal, S. R. (1975). Allocation of observations in ranking and selection with unknown variances,Sankhyã, B37, 28–78.MathSciNetMATHGoogle Scholar
  6. [6]
    Dudewicz, E. J., Ramberg, J. S. and Chen, H. J. (1975). New tables for multiple comparisons with a control (unknown variances),Biomet. J.,17, 13–26.MathSciNetMATHGoogle Scholar
  7. [7]
    Dudewicz, E. J. and Taneja, V. S. (1978). Multivariate ranking and selection without reduction to a univariate problem,Proceedings of the 1978 Winter Simulation Conference (eds. H. J. Highland, N. R. Nielsen and L. G. Hull), 207–210.Google Scholar
  8. [8]
    Dudewicz, E. J. and Taneja, V. S. (1981). A multivariate solution of the multivariate ranking and selection problem,Commun. Statist., A10, 1849–1868.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Dudewicz, E. J. and Taneja, V. S. (1985). New directions in multivariate statistical analysis and statistical computing,Bull. Internat. Statist. Inst.,51, 19.1-1–19.1-15.Google Scholar
  10. [10]
    Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems,Ann. Eugen.,7, 179–188.Google Scholar
  11. [11]
    Hyakutake, H. (1985). A construction method of certain matrices required in the multivariate heteroscedastic method,Technical Report, No. 149, Statistical Research Group, Hiroshima University, Japan.Google Scholar
  12. [12]
    Hyakutake, H. and Siotani, M. (1984). Distributions of some statistics in heteroscedastic inference method,Technical Report, No. 108, Statistical Research Group, Hiroshima University, Japan.Google Scholar
  13. [13]
    Hyakutake, H., Siotani, M., Li, C.-Y and Mustafid (1984). Distributions of some statistics in heteroscedastic inference method II: Tables of percentage points and power functions,Technical Report No. 142, Statistical Research Group, Hiroshima University, Japan.Google Scholar
  14. [14]
    Ruben, H. (1962). Studentisation of two-stage sample means from normal populations with unknown variances. I. General theory and application to the confidence estimation and testing of the differences in population means,Sankhyã, A24, 157–180.MathSciNetMATHGoogle Scholar
  15. [15]
    Siotani, M., Hyakutake, H., Li, C.-y. and Mustafid (1985). Simultaneous confidence intervals with a given length for mean vectors constructed by the heteroscedastic method,Technical Report No. 152, Statistical Research Group, Hiroshima University, Japan.Google Scholar
  16. [16]
    Stein, C. M. (1945). A two-sample test for a linear hypothesis whose power is independent of the variance,Ann. Math. Statist.,16, 243–258.MATHGoogle Scholar
  17. [17]
    Wilcox, R. R. (1984). A review of exact hypothesis testing procedures (and selection techniques) that control power regardless of the variances,Brit. J. Math. Statist. Psychol.,37, 34–48.MathSciNetMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1987

Authors and Affiliations

  • Edward J. Dudewicz
    • 1
    • 2
  • Vidya S. Taneja
    • 1
    • 2
  1. 1.Syracuse UniversitySyracuseUSA
  2. 2.Western Illinois UniversityUSA

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