Performance of LASSO and Elastic net estimators in Misspecified Linear Regression Model

Abstract

Ridge Estimator (RE) has been used as an alternative estimator for Ordinary Least Squared Estimator (OLSE) to handle multicollinearity problem in the linear regression model. However, it introduces heavy bias when the number of predictors is high, and it may shrink irrelevant regression coefficients, but they are still in the model. Least Absolute Shrinkage and Selection Operator (LASSO) and Elastic net (Enet) estimator have been used to make the variable selection and shrinking the regression coefficients simultaneously. Further, the model misspecification due to excluding relevant explanatory variable in the linear regression model is considered as a severe problem in statistical research, and it will lead to bias and inconsistent parameter estimation. The performance of RE, LASSO and Enet estimators under the correctly specified regression model was well studied in the literature. This study intends to compare the performance of RE, LASSO and Enet estimators in the misspecified regression model using Root Mean Square Error (RMSE) criterion. A Monte-Carlo simulation study was used to study the performance of the estimators. In addition to that, a real-world example was employed to support the results. The analysis revealed that Enet outperformed RE and LASSO in both correctly specified model and misspecified regression model.