Testing hypotheses concerning unions of linear subspaces

Roger L. Berger, Dennis F. Sinclair

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


The likelihood ratio test (LRT) for hypotheses concerning unions of linear subspaces is derived for the normal theory linear model. A more powerful test, an intersection-union test, is proposed for the case in which the subspaces are not all of the same dimension. A theorem is proved that may be used to identify hypotheses that concern unions of linear subspaces. Some hypotheses about the spacings between normal means are shown to concern unions of linear subspaces and therefore can be tested using the LRT. Finally, the computation of the LRT statistic is discussed.

Original languageEnglish (US)
Pages (from-to)158-163
Number of pages6
JournalJournal of the American Statistical Association
Issue number385
StatePublished - Mar 1984


  • Intersection-union test
  • Likelihood ratio test
  • Linear model
  • Ordered means
  • Spacings between means

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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