Application of least squares variance component estimation to errors-in-variables models
Application of least squares variance component estimation to errors-in-variables models
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DOI：
10.1007/s00190-013-0658-8
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发表时间：
2013-10
影响因子：
4.4
通讯作者：
A. Amiri-Simkooei
中科院分区：
文献类型：
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作者：
A. Amiri-Simkooei
在早期的工作中，提出了加权总体最小二乘 (WTLS) 问题的简单而灵活的公式。该公式允许人们直接将最小二乘理论的现有知识体系应用于变量误差（EIV）模型，其中可以采用观察向量和设计矩阵的协方差矩阵的完整描述。这一贡献提出了针对总最小二乘问题的著名理论之一——最小二乘方差分量估计（LS-VCE）。采用 LS-VCE 来处理 EIV 模型中不同方差分量的估计，该模型具有从函数自变量的（完全填充的）协方差矩阵获得的一般协方差矩阵以及误差传播定律的正确应用。提出了两个使用真实数据和模拟数据的实证例子来说明该理论。第一个示例是线性回归模型，第二个示例是二维仿射变换。对于每个应用，同时估计两个方差分量——一个用于观测向量，一个用于系数矩阵。由于该公式基于标准最小二乘理论，因此还可以呈现一般估计的协方差矩阵以及特定估计的精度。
In an earlier work, a simple and flexible formulation for the weighted total least squares (WTLS) problem was presented. The formulation allows one to directly apply the existing body of knowledge of the least squares theory to the errors-in-variables (EIV) models of which the complete description of the covariance matrices of the observation vector and of the design matrix can be employed. This contribution presents one of the well-known theories—least squares variance component estimation (LS-VCE)—to the total least squares problem. LS-VCE is adopted to cope with the estimation of different variance components in an EIV model having a general covariance matrix obtained from the (fully populated) covariance matrices of the functionally independent variables and a proper application of the error propagation law. Two empirical examples using real and simulated data are presented to illustrate the theory. The first example is a linear regression model and the second example is a 2-D affine transformation. For each application, two variance components—one for the observation vector and one for the coefficient matrix—are simultaneously estimated. Because the formulation is based on the standard least squares theory, the covariance matrix of the estimates in general and the precision of the estimates in particular can also be presented.