PARAMETER ESTIMATION OF LINEAR REGRESSION MODEL WITH MULTICOLLINEARITY AND HETEROSCEDASTICITY PROBLEMS

Abstract

It is very obvious that the assumption of the classical linear regression model are rarely fulfilled in real life situation. The violation of assumption of independent regressors and equal error variances leads to the problems of multicollinearity and heteroscedasticity respectively. In practice, both problems do exist together in a data set. Most of the developed existing estimators addressed each problem separately. Usually, one of the problems is handled while the other is left uncared for. Estimators to handle the two problems jointly are hardly common. There is therefore a need to develop estimators that can handle parameter estimation even when there is multicollinearity and heteroscedasticity. Consequently, this paper proposed estimators to handle parameter estimation of linear regression model having both multicollinearity and heteroscedasticity problems with the aim of identifying the most efficient (best) when both are in existence. The Ordinary least squares (OLS) estimators resulted to the weighted Least Squares model with Heteroscedasticity measures by real weight (OLSRW) and three other weights (OLSW1, OLSW2, OLSW3. Similarly, the Generalized Ridge Esimator (GRE) and the Ordinary Ridge Estimator (ORE) respectively resulted into proposed estimators GRERW, GREW1, GREW2, GREW3, ORERW, OREW1, OREW2, and OREW3. Monte carlo simulation were conducted one thousand (1000) times on a linear regression model exhibiting different levels of multicollinearity (ρ = 0.6, 0.8, 0.9, 0.99, 0.999, 0.9999 ) with various known natures of heteroscedasticity, error variances (???????????? = ????. ????????, ????. ????, ????????, ????????????, ????????????) at seven levels of sample size (n=15, 20, 30, 50, 100, 250, 500). The comparison of the estimators were done based on the their finite sampling properties especially the mean squares error, and were compared at each level of multicollinearity, heteroscedasticity, error variance and sample sizes. Ranking of the estimators were also conducted on the basis of their performances using the criteria. The results of investigation revealed that with known  eteroscedasticity structures present with multicollinearity problem, the proposed GRERW estimator is best. Also, when there is problem of multicollinearity with known natures of heteroscedasticity but assumed tobe unknown, the proposed estimator GREW2 performed better.