ABSTRACT

Robust estimators are widely used in regression analysis when the normality assumption is not satisfied. One example of robust estimators for regression is adaptive modified maximum likelihood (AMML) estimators [Donmez A. Adaptive estimation and hypothesis testing methods [dissertation]. Ankara: METU; 2010]. However, they are not robust to x outliers, so-called leverage points. In this study, we propose a new estimator called robust AMML (RAMML) which 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 estimators with some existing robust estimators. The results show that the RAMML estimators are preferable in most of the 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.

摘要

当不满足正态性假设时，稳健估计器将广泛用于回归分析。用于回归的鲁棒估计量的一个示例是自适应修正最大似然（AMML）估计量[Donmez A.自适应估计和假设检验方法[论文]。安卡拉：METU；2010]。但是，它们对于x个离群点（所谓的杠杆点）不具有鲁棒性。在这项研究中，我们提出了一种新的估计器，称为鲁棒AMML（RAMML），它不仅对y异常值而且对x鲁棒离群值。进行了仿真研究，以将RAMML估计器的性能与一些现有的鲁棒估计器进行比较。结果表明，根据均方误差（MSE）准则，RAMML估计器在大多数设置中均更可取。还对来自文献的两个数据集进行了分析，以显示RAMML估算方法的实现。