Variance component estimation in errors-in-variables models and a rigorous total least-squares approach
Variance component estimation in errors-in-variables models and a rigorous total least-squares approach
复制标题
DOI：
10.1007/s11200-013-1150-x
复制
发表时间：
2013
影响因子：
0.9
通讯作者：
V. Mahboub
中科院分区：
文献类型：
--
作者：
V. Mahboub
提出了一种用于变量误差（EIV）模型的方差分量估计（VCE）方法，从而得到一种新的严格总体最小二乘（TLS）方法。为了实现一个现实的参数估计，知识的随机模型，除了功能模型，是必需的。对于EIV模型，现有的TLS技术要么根本不考虑随机模型，要么假设近似模型，例如只有一个方差分量的模型。与这种TLS技术相比，所提出的方法考虑了EIV模型调整中随机模型的未知结构。它同时预测随机模型和估计函数模型的未知参数。此外，该方法显示了EIV模型如何在某些情况下支持Gauss-Helmert模型。为了使VCE理论在EIV模型中的应用更具有实用性，本文还提出了两种简化算法。所提方法可用于线性回归和数据转换。我们将这些方法应用到这些例子中。具体地，执行3-D非线性接近相同的相似性变换。两个模拟研究，除了一个实验的例子给洞察算法的效率。
A method for variance component estimation (VCE) in errors-in-variables (EIV) models is proposed, which leads to a novel rigorous total least-squares (TLS) approach. To achieve a realistic estimation of parameters, knowledge about the stochastic model, in addition to the functional model, is required. For an EIV model, the existing TLS techniques either do not consider the stochastic model at all or assume approximate models such as those with only one variance component. In contrast to such TLS techniques, the proposed method considers an unknown structure for the stochastic model in the adjustment of an EIV model. It simultaneously predicts the stochastic model and estimates the unknown parameters of the functional model. Moreover the method shows how an EIV model can support the Gauss-Helmert model in some cases. To make the VCE theory into EIV model more applicable, two simplified algorithms are also proposed. The proposed methods can be applied to linear regression and datum transformation. We apply these methods to these examples. In particular a 3-D non-linear close to identical similarity transformation is performed. Two simulation studies besides an experimental example give insight into the efficiency of the algorithms.