Abstract

The least-squares (LS) is a known estimator for the estimation of the linear regression model parameter. The LS is inefficient in the happening of the significant correlations among the explanatory variables. Alternatively, we propose a new regression estimator for the purpose of the reduction of multicollinearity effects. The comparisons between the new regression estimator with each of the available regression estimators are performed theoretically. Then, a massive simulation with different factors is done. The main finding point of this study is that the new regression estimator is superior to other available regression estimators under some determined conditions using the mean squared error. Finally, a numerical example is also done to ensure the superiority of the new regression estimator.

摘要

最小二乘法（LS）是用于估计线性回归模型参数的已知估计器。LS 在解释变量之间发生显着相关性方面效率较低。或者，我们提出了一种新的回归估计器，以减少多重共线性效应。新回归估计器与每个可用回归估计器之间的比较是在理论上进行的。然后，进行不同因素的大规模模拟。这项研究的主要发现点是，在某些使用均方误差的确定条件下，新的回归估计器优于其他可用的回归估计器。最后还通过数值算例验证了新回归估计器的优越性。