Abstract

The issue of heteroscedasticity and its adverse impact on the estimation of a linear regression model has been extensively discussed in the available literature. Some adaptive estimators have also been proposed in the context of weighted least squares (WLS) to address the issue. Estimation of linear regression model becomes more challenging when the issue of heteroscedasticity is bundled together with the presence of outliers. In the present article, we use a relatively latest approach that is the least squares ratio method to estimate a linear regression model in the presence of heteroscedasticity and outliers. We propose an adaptive version of this technique while taking advantage of some existing adaptive estimators to fix the issue of unknown heteroscedasticity. A Monte Carlo evidence has been presented for the performance of the stated estimator varying degree of heteroscedasticity and number of outliers.

摘要

现有文献中已广泛讨论了异方差问题及其对线性回归模型估计的不利影响。在加权最小二乘法（WLS）的背景下也提出了一些自适应估计器来解决这个问题。当异方差问题与异常值的存在捆绑在一起时，线性回归模型的估计变得更具挑战性。在本文中，我们使用一种相对最新的方法，即最小二乘比法来估计存在异方差和异常值的线性回归模型。我们提出了该技术的自适应版本，同时利用一些现有的自适应估计器来解决未知异方差性的问题。