Some results on parameter estimation in extended growth curve models. (English) Zbl 0951.62045

Summary: Estimation of parameters in extended growth curve models with arbitrary covariance matrix or uniform covariance structure or serial covariance structure is studied. Admissibility and minimaxity of the least-squares estimator of regression coefficients under matrix loss are derived. The necessary and sufficient existence conditions are obtained for the uniformly minimum risk equivariant (UMRE) estimator of regression coefficients under an affine group and a transitive group of transformations with quadratic loss and matrix loss, respectively. It is proved that no UMRE estimators of the covariance matrix \(V\) and the trace of \(V\) exist. The maximum likelihood estimator of parameters under some conditions is also discussed.


62H12 Estimation in multivariate analysis
62C15 Admissibility in statistical decision theory
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