  Let $\mathbf{Y}=\mathbf{X}\bolds{\Theta}\mathbf{Z}'+\bolds{\mathcal {E}}$ be
the growth curve model with $\bolds{\mathcal{E}}$ distributed with mean
$\mathbf{0}$ and covariance $\mathbf{I}_n\otimes\bolds{\Sigma}$, where
$\bolds{\Theta}$, $\bolds{\Sigma}$ are unknown matrices of parameters and
$\mathbf{X}$, $\mathbf{Z}$ are known matrices. For the estimable parametric
transformation of the form $\bolds
{\gamma}=\mathbf{C}\bolds{\Theta}\mathbf{D}'$ with given $\mathbf{C}$ and
$\mathbf{D}$, the two-stage generalized least-squares estimator $\hat{\bolds
\gamma}(\mathbf{Y})$ defined in (7) converges in probability to $\bolds\gamma$
as the sample size $n$ tends to infinity and, further,
$\sqrt{n}[\hat{\bolds{\gamma}}(\mathbf{Y})-\bolds {\gamma}]$ converges in
distribution to the multivariate normal distribution $\ma
thcal{N}(\mathbf{0},(\mathbf{C}\mathbf{R}^{-1}\mathbf{C}')\otimes(\mat
hbf{D}(\mathbf{Z}'\bolds{\Sigma}^{-1}\mathbf{Z})^{-1}\mathbf{D}'))$ under the
condition that $\lim_{n\to\infty}\mathbf{X}'\mathbf{X}/n=\mathbf{R}$ for some
positive definite matrix $\mathbf{R}$. Moreover, the unbiased and invariant
quadratic estimator $\hat{\bolds{\Sigma}}(\mathbf{Y})$ defined in (6) is also
proved to be consistent with the second-order parameter matrix
$\bolds{\Sigma}$.
