附有奇异值修正限制的改进的岭估计方法
发布时间：2018-08-25 19:21
【摘要】：最小二乘估计具有无偏性,而岭估计是一种有偏估计,它通过引入偏差降低方差来降低均方误差。在模型出现病态时,岭估计优于最小二乘估计。对岭估计的方差与偏差进行分析发现,岭估计通过修正病态矩阵的奇异值降低均方误差,但对部分较大奇异值的修正不能有效降低均方误差。通过比较修正奇异值的方差下降量与偏差引入量的大小关系确定需要修正的小奇异值,进而改进岭估计方法,实现选择性地修正小奇异值,提出附有奇异值修正限制的改进的岭估计方法,可有效改善岭估计的解算效果和可靠性,实验验证了新方法的可行性和有效性。
[Abstract]:The least square estimation is unbiased, while the ridge estimation is a kind of biased estimation, which reduces the mean square error by introducing the deviation to reduce the variance. When the model is ill-conditioned, the ridge estimation is superior to the least square estimation. By analyzing the variance and deviation of ridge estimation, it is found that ridge estimation reduces mean square error by modifying singular value of ill-conditioned matrix, but correction of partial larger singular value can not effectively reduce mean square error. By comparing the relationship between the variance drop of the modified singular value and the deviation introduced quantity, the small singular value that needs to be modified is determined, and then the ridge estimation method is improved to realize the selective correction of the small singular value. An improved ridge estimation method with singular value correction constraints is proposed, which can effectively improve the solution effect and reliability of the ridge estimation. The experimental results show that the new method is feasible and effective.
【作者单位】： 中南大学地球科学与信息物理学院;
【基金】：国家自然科学基金(41531068,41474008) 国家重点基础研究发展计划(2013CB733303)~~
【分类号】：P207
本文编号：2203857
[Abstract]:The least square estimation is unbiased, while the ridge estimation is a kind of biased estimation, which reduces the mean square error by introducing the deviation to reduce the variance. When the model is ill-conditioned, the ridge estimation is superior to the least square estimation. By analyzing the variance and deviation of ridge estimation, it is found that ridge estimation reduces mean square error by modifying singular value of ill-conditioned matrix, but correction of partial larger singular value can not effectively reduce mean square error. By comparing the relationship between the variance drop of the modified singular value and the deviation introduced quantity, the small singular value that needs to be modified is determined, and then the ridge estimation method is improved to realize the selective correction of the small singular value. An improved ridge estimation method with singular value correction constraints is proposed, which can effectively improve the solution effect and reliability of the ridge estimation. The experimental results show that the new method is feasible and effective.
【作者单位】： 中南大学地球科学与信息物理学院;
【基金】：国家自然科学基金(41531068,41474008) 国家重点基础研究发展计划(2013CB733303)~~
【分类号】：P207
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