Abstract

Let be the extended growth curve model with error matrix ℰ distributed as a normal distribution with mean 0 and covariance I⊗ Σ, subject to some specified conditions. A quadratic statistic Σˆ(Y), distributed as a Wishart distribution, is proposed and proved to be a uniformly minimum variance unbiased invariant estimator of the second-order parameter matrix Σ. In addition, unbiased and explicit estimators Θˆ i (Y) of the first-order parameter matrices Θ i are given. And explicit formulae to compute the traces of the covariance matrices of Θˆ i (Y) are derived.

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