On some two parameter estimators for the linear regression models with correlated predictors: simulation and application

Regression analysis is widely used to predict the response variable utilizing one or more predictor variables. In many fields of study, the predictors are highly correlated causing multicollinearity problem that severely affects the efficiency of ordinary least square (OLS) estimators by significantly inflating their variances. To solve the multicollinearity problem, various one and two parameter ridge estimators are available in literature. In this article, a class of modified two parameter Lipovetsky-Conklin ridge estimators is proposed based on eigen values of X ' X matrix that provide an automatic dealing option for treating different levels of multicollinearity. An extensive simulations study followed by real life example is used to evaluate the performance of proposed estimators based on MSE criterion. In most of the simulation conditions, our proposed estimators outperformed the existing estimators.