| 关于加权全最小一乘法 |
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| 引用本文： | 冯守平,杨桂元.关于加权全最小一乘法[J].应用概率统计,2009,25(2):135-142. |
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| 作者姓名： | 冯守平 杨桂元 |
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| 作者单位： | 安徽财经大学统计与应用数学学院,蚌埠,233030 |
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| 基金项目： | 安徽省教育厅自然科学基金 |
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| 摘 要： | 本文证明了在准则$Q(a,b,c)=\frac{1}{\sqrt{a^2+b^2}}\tsm_{i=1^nw_i|ax_i+by_i+c|=\min\qq(w_i>0,\,i=1,2,\cdots,n)$下, 最优直线$ax+by+c=0$的存在性,并给出了最优直线应满足的两个必要条件, 为具体求出确切的最优解提供了依据和方法.
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| 关 键 词： | 加权全最小一乘法 最优直线 存在性 必要条件. |
On Weighted Total Least Absolute Deviations |
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| FENG SHOUPING,YANG GUIYUAN.On Weighted Total Least Absolute Deviations[J].Chinese Journal of Applied Probability and Statisties,2009,25(2):135-142. |
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| Authors: | FENG SHOUPING YANG GUIYUAN |
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| Institution: | School of Statistics and Applied Mathematics, Anhui University of Finance and Economics |
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| Abstract: | The paper demonstrates the existence of the optimal straight line under the minimum of weighted total least absolute deviation, and suggests the two necessary conditions that the optimal straight line should satisfy, and provides evidence for the calculation of accurate and optimal solution. |
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| Keywords: | Weighted total least absolute deviations optimal straight line existence necessary conditions |
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