Combined estimators as alternative to multicollinearity estimation methods

The use of Ordinary Least Square (OLS) estimator for estimation of parameters of linear regression model in the presence of multicollinearity has been reported to produce imprecise estimates associated with large standard errors. This paper presents some combined estimators based on Feasible Generalized Linear Estimator (CORC and ML) and Principal Components (PCs) Estimator as alternative to multicollinearity estimation methods. A linear regression model with three uniformly distributed explanatory variables exhibiting high degree of multicollinearity ( ) was considered through Monte Carlo studies. The experiments were conducted to assess and compare the performances of the various proposed combined estimators with their separate ones and the Ridge estimator using the Mean Square Error (MSE) criterion by ranking their performances at each parameter level and summing the ranks over the number of parameters. Results reveal that the proposed estimators of CORCPC1, MLPC1 and MLPC12 are generally better than the OLS estimator while CORCPC12 does the same at increased sample size. Furthermore, the combined estimator CORCPC1, recommended for usage, performs better than the Ridge estimator and it is either the best or does not perform too differently from the PC1 or PC12 estimator.