| 以减小均方误差为目标的估计 |
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| 引用本文： | 顾勇为,归庆明.以减小均方误差为目标的估计[J].信息工程大学学报,2010,11(3):364-367. |
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| 作者姓名： | 顾勇为 归庆明 |
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| 作者单位： | 1. 信息工程大学,测绘学院,河南,郑州,450052;信息工程大学,理学院,河南,郑州,450001
2. 信息工程大学,理学院,河南,郑州,450001 |
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| 基金项目： | 国家自然科学基金资助项目，河南省基础与前沿技术研究计划资助项目 |
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| 摘 要： | 文章分析了病态问题的特点，提出此时以最小方差为估计准则的LS估计常不能获得稳定的解，另一比较奏效的估计准则是均方误差最小。提出了均方误差意义下的最优线性估计，将其与正则化估计对照，获得了对正则化估计更加深入的认识，而正则化估计在均方误差意义下是优于最小二乘估计的。提出了基于正则化估计的单位权方差的无偏估计公式。
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| 关 键 词： | 均方误差 最优线性估计 正则化估计 单位权方差 |
Estimation Aiming at Reducing Mean Squared Errors |
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| GU Yong-wei,GUI Qing-ming.Estimation Aiming at Reducing Mean Squared Errors[J].Journal of Information Engineering University,2010,11(3):364-367. |
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| Authors: | GU Yong-wei GUI Qing-ming |
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| Affiliation: | 1. Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450052, China; 2. Institute of Science, Information Engineering University, Zhengzhou 450001, China) |
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| Abstract: | In this paper the character of ill-posed problem is analyzed in detail, the estimation criterion of the least variance is sometimes no longer a proper criterion, as the least square estimation is rather unstable. Another effective criterion is the least mean squared errors. The best linear estimation in the sense of the least mean squared errors is put forword. The comparison between it and regularization has been made, a deep recognizion to regularization is obtained, and the regularization is superior to the least square estimation in the sense of the least mean squared errors. The unbiased estimation formula of unit weight mean square error in the regularization solution is derived. |
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| Keywords: | mean squared errors the best linear estimation regularization mean square of unit weight |
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