EXAMINING ALKHAMISI RIDGE ESTIMATOR IN DIFFERENT TYPES VARIOUS FORMS AND KINDS USING MONTE CARLO STUDY

Statistics

Abstract The existence of high correlations between two or more exogenous variables in regression can lead to a serious multicolinearity problem. Multicollinearity influences the ordinary least squares estimator in producing inefficient estimates. 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 in proposing 228 new ridge parameters. The existing and proposed ridge estimators (228) were compared through Monte Carlo simulation experiment 1000 times on a linear regression model with three (3) exogenous variables (), taking ( and seven (7) predictor variables (), taking that exhibited different degrees of multicollinearity: , standard error and six sample sizes: At , the problem of multicollinearity existed which was pronounced and corrected at . In order to identify the proposed ridge estimators with most efficient estimates, their individual performances were compared with the existing results via mean square error criterion. 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, which is a proposed estimator.

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