An adaptive weighted least squares ratio approach for estimation of heteroscedastic linear regression model in the presence of outliers

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.

Automated summary

This article extensively discusses the issue of heteroscedasticity and its negative impact on linear regression model estimation. It introduces a relatively new approach called the least squares ratio method to estimate a linear regression model in the presence of heteroscedasticity and outliers. An adaptive version of this technique is proposed, taking advantage of existing adaptive estimators to address the issue of unknown heteroscedasticity. Monte Carlo simulation is used to evaluate the performance of the proposed estimator under varying degrees of heteroscedasticity and number of outliers.