A MONTE CARLO STUDY OF ALKHAMISI RIDGE ESTIMATOR

Abstract

In classical linear regression model, the existence of high correlations between two or more exogenous variables results to multicollinearity problem. This problem influences the ordinary least squares (OLS) estimator in producing inefficient estimates of the model parameters. Based on the aforementioned, application of ridge regression to obtain ridge parameter that will produce efficient estimates in the presence of multicollinearity becomes necessary. Several authors have studied modalities of setting ridge parameters that will give best estimates of the model parameters. This research work examined the ridge parameter estimation techniques of Alkhamisi ridge estimator, which has already been examined in different forms and in various types by some authors. However, the concept of various kinds of ridge estimators was introduced into the classification of Alkhamisi ridge parameter; this now resulted into proposing 228 new ridge parameters. The existing and proposed (228) ridge parameters were compared by conducting Monte Carlo simulation experiment 1000 times on a linear regression model with three (3) predictor variables (p=3), taking 𝛽0 = 0, 𝛽1 = 0.8, 𝛽2 = 0.1, 𝛽3 = 0.6. and seven (7) predictor variables (p=7), taking 𝛽0 = 0, 𝛽1 = 0.4, 𝛽2 = 0.1, 𝛽3 = 0.6, 𝛽4 = 0.2, 𝛽5 = 0.25, 𝛽6 = 0.3, 𝛽7 = 0.53, that exhibited different degrees of multicollinearity (ρ = 0.8, 0.9, 0.95, 0.99, 0.999, 0.9999), error variance (σ2 = 0.25, 1, 25) and six levels of sample size(n = 20, 30, 50, 100, 150, 250). At p=3, the problem of multicollinearity existed which was pronounced and corrected at p=7. In order to identify the proposed ridge estimators with most efficient estimates, their performances were compared with the existing results via mean square error criterion (MSE). From the results, it was noticed that the proposed estimators were among those that provided efficient estimates; some of them also performed better than the existing ones even after applying to simulated and real-life data. The best ridge parameter is K4FM1R.