An Improved Beta Ridge-Type Estimator For Regression Problem

Abstract

The shrinkage-based estimators have been shown to be effective in regression problems such as multicollinearity which voids the independently identically distributed (IID) assumption on which most regression analysis is based. Estimation based on minimizing the sum of squares is not satisfactory because it is practically impossible to interpret the regression coefficient estimates optimally. The ridge parameter and other shrinkage parameters can be applied to improve the efficiency of the estimators when the explanatory variables are too related. We proposed a modified estimator for the beta regression by augmenting the ridge parameter to optimize industrial and traditional processes, modelling the dependence of a continuous random variable that assumes values in the standard unit interval [0,1], called the beta modified ridge-type estimator (BMRT) to cushion the effect of multicollinearity. Finally, simulation and real-life data are used to show the advantages of the proposed estimator over similar existing ones.