| 基于加权整体最小二乘的多元线性回归分析 |
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| 引用本文： | 文国仓,;田晓程. 基于加权整体最小二乘的多元线性回归分析[J]. 青海大学学报, 2014, 0(4): 84-87 |
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| 作者姓名： | 文国仓, 田晓程 |
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| 作者单位： | [1]青海省国土规划研究院,青海西宁810001; [2]青海省测绘地理信息局,青海西宁810001 |
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| 摘 要： | 针对变形监测数据中自变量和因变量观测向量都含有误差、且采用一般最小二乘估计是有偏的这一问题,引入EIV模型,并顾及各自变量观测精度的不同,采用加权整体最小二乘对待估参数进行估计。长江三峡库区滑坡监测实验表明,基于加权整体最小二乘的多元线性回归分析能更好地对回归方程进行参数估计,可明显提高形变预测精度。
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| 关 键 词： | 多元线性回归分析 EIV模型 整体最小二乘 变形监测 |
Multiple linear regression analysis based on weighted total least squares |
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| Affiliation: | WEN Guocang, TIAN Xiaocheng(1. Land Planning and Research Institute of Qinghai Province, Xining 810001 ,China; Surveying and Mapping Geographic Information Bureau of Qinghai Province, Xining 810001 ,China) |
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| Abstract: | In deformation monitoring data, independent variables and induced variables observation vector all contain errors, and using the general least squares estimation is biased. To solve this problem, this paper introduces a more reasonable EIV （ Error - In - Variables） model, taking into account their different variables observation precision, this paper using the weighted total least squares （WTLS） to estimate the parameters. Landslide in Three Gorges Reservoir monitoring experiments shows that the analysis based on WTLS can estimate the parameters of the regression equation better and the accuracy of deformation prediction is significantly improved. |
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| Keywords: | multiple linear regression analysis error - in - variables model total least squares deformation monitoring |
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