A modified mathematical programming model for selecting generalized ridge regression parameter / Aya Rezkallah Mohamed Ahmed Farag ; Supervised Ramadan Hamed , Ragaa Kassem

Thesis (Ph.D.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics

Ridge Regression is a biased estimation technique that adds positive constant i.e. ridge parameter, to the main diagonal element of the correlation matrix among the explanatory variables, this technique leads to better estimators. It is called generalized ridge regression when there is separate ridge parameter for each explanatory variable. Most of the ridge parameters selection techniques calculate the value of the ridge parameter depending on minimizing the Mean Square Error function (MSE) of the ridge estimators. But minimizing the prediction error function of the ridge estimators is also an important concern in case of having multicollinearity problem. Therefore, this study is concerned with estimating the values of the ridge parameters that minimize the two errors, mean square error and prediction error function of the ridge estimators in order to compute the targeted ridge parameters in the generalized ridge regression case. A mathematical programming model is deduced to estimate the generalized ridge regression parameters. The performance of the proposed mathematical programming model is evaluated and compared to the previously introduced methods through a simulation study and using a numerical example. The proposed mathematical programming model yields ridge estimators having minimum prediction error value with small mean square error value

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