| 均方误差意义下正则化解优于最小二乘解的条件 |
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| 引用本文： | 徐天河,杨元喜.均方误差意义下正则化解优于最小二乘解的条件[J].武汉大学学报(信息科学版),2004,29(3):223-226. |
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| 作者姓名： | 徐天河 杨元喜 |
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| 作者单位： | 西安测绘研究所,西安市雁塔路中段1号,710054 |
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| 基金项目： | 国家杰出青年基金资助项目 ( 4 982 5 10 7)，国家自然科学基金资助项目 ( 4 0 2 740 0 2 ) |
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| 摘 要： | 利用矩阵理论导出了均方误差意义下正则化解优于最小二乘解的条件，构造了相应的检验统计量，推导出的条件式及其相应的假设检验适合于各种正则化矩阵类型的Tikhonov正则化方法。
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| 关 键 词： | 均方误差 正则化 最小二乘 假设检验 不适定方程 解 |
| 文章编号： | 1671-8860(2004)03-0223-04 |
| 修稿时间： | 2003年12月10 |
Condition of Regularization Solution Superior to LS Solution Based on MSE Principle |
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| XU Tianhe,YANG Yuanxi.Condition of Regularization Solution Superior to LS Solution Based on MSE Principle[J].Geomatics and Information Science of Wuhan University,2004,29(3):223-226. |
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| Authors: | XU Tianhe YANG Yuanxi |
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| Institution: | XU Tianhe 1 YANG Yuanxi 1 |
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| Abstract: | The condition of regularization solution superior to LS solution is deduced on the basis of the MSE principle. A statistic for testing this condition is constructed. If the null hypothesis is accepted with a significance level, it indicates that regularization solution is superior to LS solution, which also verifies that the determined regularization matrix and regularization factor are reasonable. On the contrary, if the null hypothesis is rejected, it means that the regularization method is unreasonably used. Since the regularization matrix and regularization factor is variant and can be changed,we can modify their values until the null hypothesis is accepted. The condition and its statistic given in this paper are fit for all kinds of Tikhonov regularization methods. |
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| Keywords: | regularization method mean squared error hypothesis testing |
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