Asymptotic distributions of the MLE's and the LR test in the growth curve model with a serial covariance structure
The model considered in this paper is given by \(Y=A\Xi B+E\), \(N\times p\), where the rows of E are iid as \(N_ p(\cdot,\Sigma)\) and the covariance matrix \(\Sigma\) of the errors has the special structure of \(\Sigma =\sigma^ 2G(\rho)=\sigma^ 2(\rho^{| i-j|})\). By applying the theory of asymptotic expansions, the authors obtained the terms of the order \(N^{-1/2}\) in the asymptotic expansions of the distributions of the MLE of the parameters \(\sigma^ 2\) and \(\rho\), and consequently that of \(\Xi\) as well as the LR test.
generalized multivariate analysis of variance
scientific article; zbMATH DE number 4194923