Combined Parameters Estimation Methods of Linear Regression Model with Multicollinearity and Autocorrelation

Abstract

Multicollinearity and autocorrelation are two major problems often encounter in regression analysis. Estimators for their separate investigation have been developed even though they are not without challenges. However, the two problems occasionally do occur together. In this paper effort is made to provide some combined estimators based on Feasible Generalized Linear Estimator (CORC and ML) and Principal Components (PCs) Estimator that estimate the parameters of linear regression model when the two problems are in the model. A linear regression model with three explanatory variables distributed normally and uniformly as well as exhibiting multicollinearity and autocorrelation was considered through Monte Carlo experiments at four levels of sample size .The experiments were conducted and the performances of the various proposed combined estimators with their separate ones and the Ridge estimator were examined and compared using the Mean Square Error (MSE) criterion by ranking their performances at each level of multicollinearity, autocorrelation and parameter. The ranks were further summed over the number of parameters. Results show that the proposed estimator MLPC1 is generally best even though the CORCPC1 and PC1 often compete favorably with it. Moreover with increased sample size, the CORCPC12 and MLPC12 are often best.