Variance-covariance component estimation based on the equivalent residuals
Variance-covariance component estimation based on the equivalent residuals
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发表时间：
2010
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通讯作者：
Bofeng Li;Y. Shen;L. Lou
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作者：
Bofeng Li;Y. Shen;L. Lou
本文首先概述了方差-协方差分量估计(VCE)理论的发展，然后利用正交分解提取等价残差，建立了VCE的基本方程，针对VCE理论中两个难以解决的深刻问题，即估计协方差矩阵的区域最优性和负定义问题，进行了探讨，并分析了相应的可能的可解方案及其复杂度。在给定初始值的基本方程的基础上，给出了Helmert、最小二乘和MINQUE VCE公式，并证明了它们与现有VCE公式的等价性。推导过程有利于我们理解VCE的本质，所有VCE公式都是相同的。最后，通过两个例子来验证所提出的观点。
The development of the variance-covariance component estimation(VCE)theory is firstly synoptically reviewed in this paper.Then the equivalent residuals are extracted by using orthogonal decomposition and the fundamental equations for VCE are established.Based on that the two profound and unresolvable problems for VCE theory,namely regional optimality and negative definition for estimated covariance matrix,are explored and the corresponding possible resolvable schemes and their complexity are analysed.Thirdly,we derive out the Helmert,least squares and MINQUE VCE formulae based on the fundamental equations with the given initial values,and additionally we also prove their equivalence with the existing VCE formulae.The procedure of derivation is beneficial for us to understand the essence of VCE that all VCE formulae are identical.Finally,two examples are performed to verify the proposed viewpoints.