Development of a Robust Generalized Least Squares Liu Estimator to Address Some Basic Assumptions Violations in Linear Regression Model

The linear regression model's parameters are frequently estimated using the ordinary least squares (OLS) estimator. When certain assumptions are met, the OLS is regarded as the best linear unbiased estimator. Nonetheless, it was discovered that the conclusions were false in a large number of documented situations when multicollinearity, autocorrelation, and heavy-tail outliers in the residual were all present. In this paper, we have developed an estimator of the parameters of linear regression model that jointly handles autocorrelation, multicollinearity, and heavy tail errors. Combining the robust M (M) estimator, the Liu estimator (LE), and the Generalized Least Squares (GLS) estimator led to the development of the new estimator, MGLE. Because it combines the best features of the GLS, LE, and M estimators, the MGLE is immune to both the three problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and a simulation study showed that the proposed estimator outperformed other estimators in most of the considered conditions in terms of mean square error. It is, therefore, recommended that researchers consider employing the MGLE estimator when autocorrelation, heavy-tail errors, and multicollinearity are jointly present in linear regression model. Overlooking these joint violations can lead to misleading inferences.