Abstract

The weighted total least-squares (WTLS) estimate for the partial EIV (PEIV) model is very susceptible to outliers. In view of outliers in observations and coefficient matrix, a robust estimate of WTLS which makes using of iteratively reweighted technique (IRTLS) for the PEIV model is developed by combining a new two-step iterated algorithm of the WTLS estimate with the sensitivity-analysis based on the robust M-estimation. The uniformly most powerful test statistics are constructed to determine the down-weighting factor and the variance of unit weight is estimated by least median squares (LMS) method possessing high break-down point. Depended on the PEIV model, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for observations when the elements of the coefficient matrix are estimated, and the second scheme is contrary. The most attractive aspect is that the suggested computational formulae are the same with the traditional robust least-squares (LS) methods. The two-dimensional affine transformation and liner fitting example are analyzed, and some comparisons are performed with different available weight functions. The proposed approach (Scheme 1) proves to be a powerful tool in detecting outliers for the PEIV model.

摘要

偏 EIV (PEIV) 模型的加权总最小二乘 (WTLS) 估计值非常容易受到异常值的影响。鉴于观察值和系数矩阵中的异常值，通过将 WTLS 估计的新两步迭代算法与基于敏感性分析的新的两步迭代算法相结合，开发了一种对 PEIV 模型使用迭代重加权技术 (IRTLS) 的 WTLS 稳健估计。关于稳健的 M 估计。构建统一最强大的检验统计量来确定下加权因子，并通过具有较高分解点的最小中值二乘法（LMS）估计单位权重的方差。根据 PEIV 模型，提出了两种不同的下加权方案。在第一种方案中，当估计系数矩阵的元素时，仅对系数矩阵进行下加权，而不对观测值进行加权，而第二种方案则相反。最吸引人的方面是建议的计算公式与传统的稳健最小二乘 (LS) 方法相同。分析了二维仿射变换和线性拟合的例子，并在不同的可用权函数下进行了一些比较。所提出的方法（方案 1）被证明是检测 PEIV 模型异常值的有力工具。分析了二维仿射变换和线性拟合的例子，并在不同的可用权函数下进行了一些比较。所提出的方法（方案 1）被证明是检测 PEIV 模型异常值的有力工具。分析了二维仿射变换和线性拟合的例子，并在不同的可用权函数下进行了一些比较。所提出的方法（方案 1）被证明是检测 PEIV 模型异常值的有力工具。