The Likelihood Ratio Test of Equality of Mean Vectors with a Doubly Exchangeable Covariance Matrix

Carlos A. Coelho, Jolanta Pielaszkiewicz

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The authors derive the LRT statistic for the test of equality of mean vectors when the covariance matrix has what is called a double exchangeable structure. A second expression for this statistic, based on determinants of Wishart matrices with a block-diagonal parameter matrix, allowed for the expression of the distribution of this statistic as that of a product of independent Beta random variables. Moreover, the split of the LRT statistic into three independent components, induced by this second representation, will then allow for the expression of the exact distribution of the LRT statistic in a very manageable finite closed form for most cases and the obtention of very sharp near-exact distributions for the other cases. Numerical studies show that, as expected, due to the way they are built, these near-exact distributions are indeed asymptotic not only for increasing sample sizes but also for increasing values of all other parameters in the distribution, besides lying very close to the exact distribution even for extremely small samples.
Original languageEnglish
Title of host publicationMethodology and Applications of Statistics: A Volume in Honor of C. R. Rao on the Occasion of his 100th Birthday
EditorsBarry C. Arnold, Narayanaswamy Balakrishnan, Carlos A. Coelho
Place of PublicationCham
Number of pages41
ISBN (Electronic)978-3-030-83670-2
ISBN (Print)978-3-030-83669-6
Publication statusPublished - Dec 2021

Publication series

NameContributions to Statistics
ISSN (Print)1431-1968


  • Asymptoticity for all parameters
  • Exact distribution
  • Near-exact distributions
  • Product of Betas
  • Quadratic space
  • Small samples


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