论文标题
线性回归模型的强大自适应修饰的最大似然估计器
A Robust Adaptive Modified Maximum Likelihood Estimator for the Linear Regression Model
论文作者
论文摘要
在线性回归中，如果误差正态分布，则最小二乘（LS）估计器具有某些最佳属性。在实践中通常会违反此假设，部分是由数据异常值引起的。强大的估计器可以应对这种情况，因此在实践中被广泛使用。回归的鲁棒估计量的一个例子是自适应修饰的最大似然（AMML）估计器（Donmez，2010年）。但是，它们对$ x $ utliers，即所谓的杠杆点并不强大。在这项研究中，我们通过在AMML估计方法中采用适当的加权方案提出了一个新的回归估计器。所得估计量称为健壮AMML（RAMML），因为它不仅对y异常值也是可靠的，而且对X异常值也是可靠的。进行了一项模拟研究，以将RAMML估计器的性能与一些现有的稳健估计器（例如MM，最小修剪正方形（LTS））进行比较。结果表明，根据大多数情况，根据平均平方误差（MSE）标准，在大多数情况下都可以使用RAMML估计器。还分析了从文献中获取的两个数据集，以显示RAMML估计方法的实现。
In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with this situation and thus they are widely used in practice. One example of robust estimators for regression are adaptive modified maximum likelihood (AMML) estimators (Donmez, 2010). However, they are not robust to $x$ outliers, so-called leverage points. In this study, we propose a new regression estimator by employing an appropriate weighting scheme in the AMML estimation method. The resulting estimator is called robust AMML (RAMML) since it is not only robust to y outliers but also to x outliers. A simulation study is carried out to compare the performance of the RAMML estimator with some existing robust estimators such as MM, least trimmed squares (LTS) and S. The results show that the RAMML estimator is preferable in most settings according to the mean squared error (MSE) criterion. Two data sets taken from the literature are also analyzed to show the implementation of the RAMML estimation methodology.
