The estimation of the weights of measured quantities within the method of least squares
The estimation of the weights of measured quantities within the method of least squares
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DOI：
10.1007/bf02521994
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发表时间：
1970-03
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影响因子：
--
通讯作者：
K. Kubik
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文献类型：
--
作者：
K. Kubik
本文提出了最小二乘方法的一种扩展：除了更常用的计算未知数外，该方法还估计了原始测量值的方差和这些方差之间的关系。最小二乘方法用于估计线性模型中未知的大小，而这一方法的基本前提是知道被测量量的“权重”。然而，这些权重通常是不充分知道的，并且假设它们的建立不可避免地导致结果的系统性偏差，其限制是难以控制的。在这种情况下，建议与模型中的其他未知数同时估计权重，这就是该方法的目的。
This paper proposes an extension of the familiar method of least squares: for in addition to the more commonly computed unknowns, the variances of the original measurements and the relationships between these variances are estimated in this method.The method of least squares serves to estimate the unknown magnitudes in linear models and the essential prerequisite for this is the knowledge of the" weights" of the measured quantities, Frequently, however, these weights are not known adequately and to establish them hypothetically inevitably leads to systematic deviations in the results, the limits of which are difficult to control. In these circumstances it is advisable to estimate the weights simultaneously with the other unknowns in the model, And such is the purpose of this method.