On the Modified Almost Unbiased Ridge Estimator in Linear Regression Model

In order to overcome the negative effects caused by multicollinearity between the explanatory variables in the linear regression model, a new estimator namely modified almost unbiased ridge estimator is presented with its statistical characteristics in this paper. Also, the matrix mean squared error and squared bias criteria are adopted as a basis for comparisons between the new estimator and the ordinary least squares estimator, ridge estimator, and almost unbiased ridge estimator. Further, selection of the biasing parameter is discussed. Moreover, to check the performance of the new estimator versus the other estimators considered in this paper in the sense of scalar mean squared error, a study of Monte Carlo simulation and a real data example are conducted. The results indicate that in terms of scalar mean squared error, the new estimator, modified almost unbiased ridge estimator outperforms the others in use. So, it can be safely used when multicollinearity exists in a linear regression model.