Combating outliers and multicollinearity in linear regression model using robust Kibria-Lukman mixed with principal component estimator, simulation and computation
Kingsley Chinedu Arum, Fidelis Ifeanyi Ugwuowo, Henrietta Ebele Oranye, T.O. Alakija, T.E. Ugah, O.C. Asogwa
Abstract
Scholars usually adopt the method of least squared to model the relationship between a response variable and two or more explanatory variables. Ordinary least squares estimator's performance is good when there is no outliers and multicollinearity in the regression model dataset. Outliers and multicollinearity can occur together in a regression model dataset and least squares estimator suffers setback when both problems subsist. This study considers developing a new estimator to address both problems. We combined the principal component estimator (PCE), M-estimator and Kibria-Lukman estimator (KLE) to derive new estimator called robust PC-KL. Robust PC-KL estimator inherits the characteristics of M-estimator, KLE, and PCE which makes it efficient in handling both problems individually and jointly. We examined the performance of the robust PC-KL estimator with other existing estimators using mean squared error (MSE) as performance evaluation criteria through simulation design and real life application. Robust PC-KL estimator outperformed other estimators compared with in this study based on theoretical comparison, simulation design and real life application by having the smallest MSE.