| 二次损失下随机回归系数和参数的线性Minimax估计 |
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| 引用本文： | 徐礼文,王松桂.二次损失下随机回归系数和参数的线性Minimax估计[J].数学年刊A辑(中文版),2005(5). |
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| 作者姓名： | 徐礼文 王松桂 |
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| 作者单位： | 北京工业大学应用数理学院，北京工业大学应用数理学院 北京 100022，北京 100022 |
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| 基金项目： | 国家自然科学基金(No.10271010)
北京市自然科学基金(No．1032001)资助的项目． |
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| 摘 要： | 对带有随机效应的一般线性模型,本文提出了随机回归系数和参数线性组合的Minimax估计问题. 在二次损失下,研究了线性估计的极小极大性.关于适当的假设,得到了可估函数的唯一线性Mjnimax 估计.
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| 关 键 词： | Minimax估计 随机回归系数 二次损失 |
THE LINEAR MINIMAX ESTIMATOR OF STOCHASTIC REGRESSION COEFFICIENTS AND PARAMETERS UNDER QUADRATIC LOSS FUNCTION |
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| XU Liwen WANG Songgui College of Applied Sciences,Beijing University of Technology,Beijing ,China. College of Applied Sciences,Beijing University of Technology,Beijing ,China..THE LINEAR MINIMAX ESTIMATOR OF STOCHASTIC REGRESSION COEFFICIENTS AND PARAMETERS UNDER QUADRATIC LOSS FUNCTION[J].Chinese Annals of Mathematics,2005(5). |
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| Authors: | XU Liwen WANG Songgui College of Applied Sciences Beijing University of Technology Beijing China College of Applied Sciences Beijing University of Technology Beijing China |
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| Institution: | XU Liwen WANG Songgui College of Applied Sciences,Beijing University of Technology,Beijing 100022,China. College of Applied Sciences,Beijing University of Technology,Beijing 100022,China. |
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| Abstract: | In this paper, the authors address the problem of the linear minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general linear model with random effects. Under quadratic loss function, the property of linear estimators is investigated. The linear minimax estimator of estimable functions, which is unique with probability 1, is obtained under appropriate hypotheses. |
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| Keywords: | Minimax estimator Stochastic regression coefficients Quadratic loss function |
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