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replicated growth curve model; covariance components; multivariate regression; asymptotic confidence region
We consider a multivariate regression (growth curve) model of the form $Y = XBZ + \varepsilon $, $\operatorname{E}\varepsilon =0$, $\operatorname{var}(\operatorname{vec}\varepsilon) = W \otimes \Sigma $, where $W = \sum _{i=1}^{k} \theta _i V_i$ and $\theta _i$’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters $\lbrace B_{ij}\rbrace $ estimating simultaneously the first and the second order parameters.
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