Testing hypotheses concerning unions of linear subspaces

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.