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This paper presents the dual specification of the least-squares method. In other words, while the traditional (primal) formulation of the method minimizes the sum of squared residuals (noise), the dual specification maximizes a quadratic function that can be interpreted as the value of sample information. The two specifications are equivalent. Before developing the methodology that describes the dual of the least-squares method, the paper gives a historical perspective of its origin that sheds light on the thinking of Gauss, its inventor. The least-squares method is firmly established as a scientific approach by Gauss, Legendre and Laplace within the space of a decade, at the beginning of the nineteenth century. Legendre was the first author to name the approach, in 1805, as “méthode des moindres carrés”, a “least-squares method”. Gauss, however, used the method as early as 1795, when he was 18 years old. Again, he adopted it in 1801 to calculate the orbit of the newly discovered planet Ceres. Gauss published his way of looking at the least-squares approach in 1809 and gave several hints that the least-squares algorithm was a minimum variance linear estimator and that it was derivable from maximum likelihood considerations. Laplace wrote a very substantial chapter about the method in his fundamental treatise on probability theory published in 1812.
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篇名 The Dual of the Least-Squares Method
来源期刊 统计学期刊(英文) 学科 医学
关键词 Least SQUARES Primal DUAL PYTHAGORAS THEOREM Noise VALUE of SAMPLE Information
年,卷(期) 2015,(7) 所属期刊栏目
研究方向 页码范围 658-664
页数 7页 分类号 R73
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节点文献
Least
SQUARES
Primal
DUAL
PYTHAGORAS
THEOREM
Noise
VALUE
of
SAMPLE
Information
研究起点
研究来源
研究分支
研究去脉
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相关学者/机构
期刊影响力
统计学期刊(英文)
半月刊
2161-718X
武汉市江夏区汤逊湖北路38号光谷总部空间
出版文献量(篇)
584
总下载数(次)
0
总被引数(次)
0
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