Multivariate regression analysis with dependent observations: conditions for the invariance of the distribution of the Lawley-Hotelling test for the model utility

L. M. Meaux, D. M. Young & Seaman Jr., J. W.
In this paper we derive necessary and sufficient conditions on the error covariance structure such that the Lawley-Hotelling statistic for testing model utility is invariant from its distribution under the usual assumption of normal i.i.d. observation vectors. We, therefore, generalize the work of Arnold (1979), Ghosh and Sinha (1980), and Tranquilli and Baldesarri (1988).