Abstract

We compared the robust methods in the general linear regression (GLR) model through simulations. The results show that the S-type estimators produce the minimum mean squared error (MSE) of the model in all samples and the minimum standard errors of the estimators of the regression coefficients in almost all samples in all situations including the normal distribution despite their modesty in the efficiency. As an addition to the classical efficiency concept, we introduce a new efficiency concept based on the MSE of the model and the standard errors of the estimators of the regression coefficients. The simulations show that the S-type estimators are superior in terms of the efficiencies based on the MSE of the model and the standard errors of the estimators of the regression coefficients in all situations including the normal distribution. At the end of the study we give three examples one of which using a hypothetical data set and the rest being real-life data examples. The S-type estimators produce the minimum MSE value in all examples and the minimum standard error values in most of them. The simulations and examples also reveal some interesting phenomena about the regression analysis and the estimators included in this study.

摘要

我们通过模拟比较了一般线性回归（GLR）模型中的稳健方法。结果表明，S 型估计量在所有样本中产生模型的最小均方误差 (MSE)，并且在所有情况（包括正态分布）的几乎所有样本中产生回归系数估计量的最小标准误差，尽管它们的效率不高。作为经典效率概念的补充，我们引入了基于模型的 MSE 和回归系数估计量的标准误差的新效率概念。模拟表明，在基于模型 MSE 的效率以及包括正态分布在内的所有情况下回归系数估计量的标准误差方面，S 型估计量均具有优越性。在研究结束时，我们给出了三个示例，其中一个使用假设的数据集，其余的是现实生活中的数据示例。S 型估计量在所有示例中产生最小 MSE 值，在大多数示例中产生最小标准误差值。模拟和示例还揭示了本研究中包含的回归分析和估计量的一些有趣现象。