Robust Regression Methods for Solving Non-Spherical Problem in Linear Regression

This study investigated the effects of non-spherical disturbance on the model parameters of some classical regression models. The aim was to examine the impacts of multicollinearity on the efficiency of classical Ordinary least squares (OLS) relative to the ridge regression (RR) and principal component regression (PCR) models. Data were simulated from a multivariate normal distribution with mean zero and variance-covariance matrix at various sample sizes 25, 50, 100, 200, 500 and 1000. To assess the asymptotic efficiency and consistency of these regression models in the presence of multicollinearity, the evaluation criteria used were the Variance, Absolute bias, Mean Square Error (MSE) and Mean Square Error of Prediction (MSEP). Results from this work showed that the RR model had smaller variance, absolute bias and MSE when it was compared with OLS. Also, the ridge estimator had the least MSEP when compared to both the OLS and PCR models. Hence, it can be concluded that the ridge estimator performed better than the OLS and PCR when explanatory variables are highly correlated.