SOME ROBUST RIDGE ESTIMATORS: A COMPARATIVE STUDY

Abstract

In the presence of multicollinearity and outliers, the Ordinary Least Square estimator is found to be inefficient due to the inflated standard errors. In this paper, some forms of Generalized Ridge regression parameters proposed by Fayose and Ayinde (2019) were combined with robust estimators to estimate the parameters of linear regression model when multicollinearity and outliers are jointly evident. Linear regression models with three and five regressors (p = 3 and p = 5), three levels of multicololinearity (???? = 0.900, 0.990 ???????????? 0.999), three levels of percentages of outliers (????1% = 5%, 10% ???????????? 20%), three levels of magnitude of outliers (???????????????????????????????????? 2 = 10, 100 ???????????? 250) and three levels of sample size (???? = 20, 40 ???????????? 100) were considered through Monte Carlo experiments. The experiments were carried out 1000 times, and the performances of these combined estimators and Ordinary Least Square were investigated and compared using the Mean Square Error (MSE) criterion. Results show that the Maximum form of Fayose and Ayindes’ modified Generalized Ridge parameter of Troskie and Chalton (1996) when combined with robust Least Absolute Deviation estimator (????̂????????????????????1 ???????????? ) consistently performed more efficiently than all other methods of parameter estimation of linear regression model considered. It also shows that increasing the sample size, the number of explanatory variables, degree of multicollinearity, the magnitude of outliers and percentage of outliers affect the efficiency of these estimators.