| 有约束错误指定模型下的优化问题 |
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| 引用本文： | 张宝学. 有约束错误指定模型下的优化问题[J]. 数学物理学报(A辑), 2003, 23(3): 327-332 |
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| 作者姓名： | 张宝学 |
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| 作者单位： | 北京理工大学应用数学系 北京100081 |
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| 基金项目： | 国家自然科学基金数学天元青年基金资助项目 (批准号 :1 0 2 2 60 2 4)，中国博士后科学基金资助项目(批准号 :2 0 0 2 0 3 1 1 80 )，复旦大学数学所非线性科学重点实验室资助项目 |
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| 摘 要： | 文［１］ 利用文［3］的结果证明了一般有约束线性模型下参数的最优估计的方差协方差阵与有约束错误指定模型下最优估计的方差协方差阵间差是非负定的充分条件［２］也是必要的。更进一步，文［4］将［1］中的定理1推广到奇异线性模型上。该文的主要目的是证明了［２］的猜想在奇异线性模型中也是正确的，同时，推广了［１］中的定理2。
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| 关 键 词： | 最佳线性无偏估计 奇异线性模型 约束 方差协方差阵 |
| 文章编号： | 1003-3998(2003)03-327-06 |
| 修稿时间： | 2001-08-14 |
Additional Remarks on a Superiority Problem in Misspecified Re stricted Singular Linear Models |
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| ZHANG Bao-Xue. Additional Remarks on a Superiority Problem in Misspecified Re stricted Singular Linear Models[J]. Acta Mathematica Scientia, 2003, 23(3): 327-332 |
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| Authors: | ZHANG Bao-Xue |
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| Abstract: | When the covariance matrix of the disturbance vector in the general linear model is misspecified, Gross, Trenkler and Liski (1998) showed Razzaghi's (1987) result that sufficient condition for nonnegative definitness of the covariance matrix difference of competing estimators is also necessary by applying a result of Kabe and Gupta (1989). Further, Zhang and Liu (2000) extended the Theorem 1 of Gross, Trenkler and Liski to the singular linear model using matrix inequality and subspace relations. The aim of this paper is to prove the conjecture which Razzaghi (1987) made is true in misspecified restricted singular linear model and strengthen Theorem 2 of Gross, Trenkler and Liski by giving the necessary and sufficient conditions for nonnegative definiteness of the covariance matrix difference in the singular linear model. |
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| Keywords: | Best linear unbiased estimator Singular linear model Restrictions Covarinance matrix. |
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