EXISTENCE OF THE UMRE ESTIMATOR IN GSOWTH CURVE MODELS
增长曲线模型中UMRE估计的存在性

For normal growth curve models with designmatrices of non-full rank and witharbitrary covariance matrix or uniform covariance structure or serial covariance structure, theexistence of the uniformly minimum risk equivariant (UMRE) estimator of parameter matricesis studied. The necessary and sufficient conditions are derived for the existence of the UMREestimator of linearly estimable function matrices of the regression coefficient matrix under anaffine group G1, and a transitive group of transformations for quadratic losses and mains losses,respectively. This extends the results given by 21] for estimating the regression coefficientmatrix in the context of design matrices of full rank. It is for the first tune proved that thereis no UMRE estimator of the covariance matrix V and the trace of V under group G1 andquadrantic losses.