Göktaş Atila, Akkuş Özge, Kuvat Aykut
Department of Statistics, Muğla Sıtkı Koçman University, Muğla, Turkey.
J Appl Stat. 2020 Aug 7;48(13-15):2457-2472. doi: 10.1080/02664763.2020.1803814. eCollection 2021.
A large and wide variety of ridge parameter estimators proposed for linear regression models exist in the literature. Actually proposing new ridge parameter estimator lately proving its efficiency on few cases seems endless. However, so far there is no ridge parameter estimator that can serve best for any sample size or any degree of collinearity among regressors. In this study we propose a new robust ridge parameter estimator that serves best for any case assuring that is free of sample size, number of regressors and degree of collinearity. This is in fact realized by choosing three best from enormous number of ridge parameter estimators performing well in different cases in developing the new ridge parameter estimator in a way of search method providing the smallest mean square error values of regression parameters. After that a simulation study is conducted to show that the proposed parameter is robust. In conclusion, it is found that this ridge parameter estimator is promising in any case. Moreover, a recent data set is used as an example for illustration to show that the proposed ridge parameter estimator is performing better.
文献中存在大量为线性回归模型提出的各种各样的岭参数估计器。实际上，最近提出新的岭参数估计器并在少数情况下证明其有效性似乎没有尽头。然而，到目前为止，还没有一种岭参数估计器能在任何样本量或任何回归变量之间的共线性程度下都表现最佳。在本研究中，我们提出了一种新的稳健岭参数估计器，它在任何情况下都能表现最佳，确保不受样本量、回归变量数量和共线性程度的影响。这实际上是通过从大量在不同情况下表现良好的岭参数估计器中选择三个最佳估计器来实现的，以搜索方法的方式开发新的岭参数估计器，从而提供回归参数的最小均方误差值。之后进行了一项模拟研究，以表明所提出的参数是稳健的。总之，发现这种岭参数估计器在任何情况下都很有前景。此外，以最近的一个数据集为例进行说明，以表明所提出的岭参数估计器表现更好。
