Comparison of Liu and two parameter principal component estimator to combat multicollinearity

Biased estimation methods like ridge regression, Liu-type regression, two-parameter regression and principal component regression have become very popular in the analysis of applied researches for health, economics, chemometrics, and social sciences in recent years. A dataset in such applied fields tends to be characterized by many independent variables on relatively fewer observations. In addition, there is a high degree of near collinearity among the explanatory variables. It is common knowledge that under these conditions, ordinary least squares estimations of regression coefficients may be very unstable, leading to very poor prediction accuracy. The aim of this article is to examine the performance of the combination of principal components regression and some biased regression estimators such as ridge, Liu and two-parameter estimators. For this reason, a real-life application is presented in which different selection methods of the biasing parameters are employed.