| 增长曲线模型中UMRE估计和UMRU估计的存在性 |
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| 引用本文： | 邓起荣,陈建宝.增长曲线模型中UMRE估计和UMRU估计的存在性[J].应用数学学报,1999,22(2):169-177. |
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| 作者姓名： | 邓起荣 陈建宝 |
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| 作者单位： | [1]云南教育学院数学系 [2]云南大学统计系 |
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| 摘 要： | 对于一般的增长曲线模型，在一般的矩阵损失和二次损失下，用统一的方法分别给出了回归系数矩阵的任一指定可估函数存在一致最小风险同变（ＵＭＲＥ）估计（分别在仿真变换群和转换变换群下）和一致最小风险无编（ＵＭＲＵ）估计的充要条件，以及所有可估函数恒存在ＵＭＲＥ估计和ＵＭＲＵ估计的允要条件。最后将结果应用于一些特殊模型。
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| 关 键 词： | 增长曲线模型 UMRE估计 UMRU估计 矩阵损失 |
THE EXISTENCE OF UMRE ESTIMATOR ANDUMRU ESTIMATOR IN GROWTH CURVE MODELS |
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| DENG QIRONG.THE EXISTENCE OF UMRE ESTIMATOR ANDUMRU ESTIMATOR IN GROWTH CURVE MODELS[J].Acta Mathematicae Applicatae Sinica,1999,22(2):169-177. |
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| Authors: | DENG QIRONG |
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| Abstract: | For general growth curve model, this paper has obtained the necessary and suf-ficient conditions for the existence of the uniformly minimum risk equivariant (UMRE) esti-mator of any given estimable function of regression coefficient matrix under an affine groupor a transitive group of transformations, and the uniformly minimum risk unbiased (UMRU)estimator of any given estimable function of regression coefficient matrix for quadratic lossesand matrix losses, respectively, by using an unified method. The necessary and sufficientconditions for the existence of UMRE estimators and UMRU estimators of all estimablefunctions are also obtained respectively. |
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| Keywords: | Normal growth curve model UMRE estimator UMRU estimator matrix loss quadratic loss |
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