Combining Lasso and Liu type estimator in the linear regression model

Abstract

The Ordinary Least Square Estimator (OLSE) has been widely used to estimate unknown parameters in the linear regression model. Since OLSE produces high variance on the estimates when multicollinearity exists among the predictor variables, the Ridge Estimator (RE) is introduced as an alternative estimator. However, RE yields heavy bias in the high dimensional linear regression models, and it also produces irrelevant predictors to the estimated model. Hence, the Least Absolute Shrinkage and Selection Operator (LASSO) has been used to ensure the variable selection as well as to handle the multicollinearity problem simultaneously. It is noted that LASSO failed to outperform RE when high multicollinearity exists among the predictor variables. Further, the LASSO estimator is unstable when the number of predictors is higher than the number of observations. Hence, the Elastic net (Enet) estimator is introduced to address this problem by combining LASSO and RE. Since Liu Estimator (LE) is an alternative estimator for RE to address multicollinearity problem, the objective of this study was to propose Liu type Elastic net estimator by combining LASSO and LE. Then, we compared the prediction performance of the Liu type Elastic net (LEnet) estimator with the Elastic net and LASSO estimators in Root Mean Square Error (RMSE) sense using the real-world examples. The results showed that LEnet outperforms the other two estimators in RMSE sense.