A New Convex Estimator Combining Ridge and Ordinary Least Squares Estimators

In the presence of high correlation between the independent variables in the linear regression model, which is known as the multicollinearity problem, the ordinary least squares estimator produce large variations in the sample. To overcome this problem, several estimators have been recommended. One of these estimators that has been proposed to reduce the impact of the multicollinearity problem was the estimator of the ridge regression, which leads to biased estimated coefficients, but it has a smaller variance than ordinary least squares estimators, which may have a smaller mean square error (MSE). In this paper, a new estimator has been proposed that combines ridge regression and ordinary least squares estimators. The performance of the recommended estimator is evaluated using the mean square error criterion after obtaining its properties. It has been shown that this estimator outperforms to both the ordinary least squares as well as the ridge regression estimators in terms of mean square error. In addition, the performance of this proposed estimator was studied by using a simulation study and a set of real data to demonstrate the theoretical results.