增长曲线模型中UMRE估计的存在性

对于设计矩阵不满秩，协方差阵任意或具有均匀结构或序列结构的正态增长曲线模型，本文讨论参数矩阵的一致最小风险同变（UMng）估计的存在性．在仿射变换群GI和转移交换群、二次损失和矩阵损失下本文分别获得存在回归系数矩阵的线性可估函数矩阵的UMRE估计的充要条件，推广了由21]给出的在设计矩阵满秩下估计回归系数矩阵的结果．本文还首次证明了在群G1和二次损失下不存在协方差阵V和trV的UMRE估计．

EXISTENCE OF THE UMRE ESTIMATOR IN GSOWTH CURVE MODELS

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.