Piradl Sajjad, Shadrokh Ali, Yarmohammadi Masoud
Department of Statistics, Payame Noor University, Tehran, Iran.
J Appl Stat. 2021 Feb 4;49(7):1663-1676. doi: 10.1080/02664763.2021.1881454. eCollection 2022.
Independence of error terms in a linear regression model, often not established. So a linear regression model with correlated error terms appears in many applications. According to the earlier studies, this kind of error terms, basically can affect the robustness of the linear regression model analysis. It is also shown that the robustness of the parameters estimators of a linear regression model can stay using the M-estimator. But considering that, it acquires this feature as the result of establishment of its efficiency. Whereas, it has been shown that the minimum Matusita distance estimators, has both features robustness and efficiency at the same time. On the other hand, because the Cochrane and Orcutt adjusted least squares estimators are not affected by the dependence of the error terms, so they are efficient estimators. Here we are using of a non-parametric kernel density estimation method, to give a new method of obtaining the minimum Matusita distance estimators for the linear regression model with correlated error terms in the presence of outliers. Also, simulation and real data study both are done for the introduced estimation method. In each case, the proposed method represents lower biases and mean squared errors than the other two methods.
线性回归模型中误差项的独立性往往无法确立。因此，具有相关误差项的线性回归模型在许多应用中都会出现。根据早期研究，这种误差项基本上会影响线性回归模型分析的稳健性。研究还表明，使用M估计量可以保持线性回归模型参数估计量的稳健性。但考虑到这一点，它是因其效率的建立而获得这一特性的。然而，已经证明，最小马氏距离估计量同时具有稳健性和效率这两个特性。另一方面，由于科克伦和奥科特调整最小二乘估计量不受误差项相关性的影响，所以它们是有效估计量。在此，我们使用非参数核密度估计方法，给出一种在存在异常值的情况下为具有相关误差项的线性回归模型获取最小马氏距离估计量的新方法。同时，针对所引入的估计方法进行了模拟和实际数据研究。在每种情况下，所提出的方法都比其他两种方法表现出更低的偏差和均方误差。
