| 广义补偿最小二乘估计及其统计性质 |
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| 引用本文： | 丁士俊,孙振冰,刘星.广义补偿最小二乘估计及其统计性质[J].大地测量与地球动力学,2006,26(4):22-26. |
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| 作者姓名： | 丁士俊 孙振冰 刘星 |
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| 作者单位： | 武汉大学测绘学院,武汉,430079;广东省汕尾红海湾经济开发试验区,汕尾,516622;重庆大学土木工程学院,重庆,400045 |
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| 摘 要： | 分析了半参数模型最小二乘解的特点,特别指出矩阵BTPB病态或奇异时,补偿最小二乘将会失效。基于线形模型岭估计原理,提出了半参数广义补偿最小二乘估计法,给出了其估计公式及其统计性质,并通过算例分析得出了相应的结论。
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| 关 键 词： | 半参数模型 补偿最小二乘 广义补偿最小二乘 病态矩阵 岭估计 |
| 文章编号： | 1671-5942(2006)04-0022-05 |
| 修稿时间： | 2006年1月20日 |
GENERAL COMPENSATED LEAST SQUARES AND ITS STATISTICAL PROPERTIES |
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| Ding Shijun,Sun Zhenbing,Liu Xing.GENERAL COMPENSATED LEAST SQUARES AND ITS STATISTICAL PROPERTIES[J].Journal of Geodesy and Geodynamics,2006,26(4):22-26. |
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| Authors: | Ding Shijun Sun Zhenbing Liu Xing |
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| Abstract: | Having analyzed the characteristics of least squares solution for semiparametric model,this paper especially points out that compensated least squares for semiparametric model will be invalid when the matrix B~TPB is ill-posed or singular.According to the principle of ridge estimate for linear parametric model,the general compensated least squares for semiparametric model is put forward,and the formula and statistical properties of estimates are given.Finally,some helpful conclusions are drawn after analyzing some examples. |
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| Keywords: | semiparametric model compensated least squares general compensated least squares ill-posed matrix ridge estimate |
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