Comparison of Test Statistics for Testing the Regression Coefficients in the OLS, Ridge, Liu, and Kibria-Lukman Linear Regression Model: A Simulation Study

Ridge, Liu and Kibria-Lukman regression are methods that have been developed to minimize the multicollinearity problem for both linear and non-linear regression models. This paper proposes some new Ridge, Liu and Kibria-Lukman regression t-type tests of the individual coefficients of a linear regression model. A simulation study was conducted to evaluate and compare the performance of the tests with respect to their empirical size and power for different levels of correlation in the data. Our simulations allow us to identify which one of the proposed tests maintains type I error rates close to the 5% nominal level, while at the same time showing considerable gain in statistical power over the standard ordinary least squares (OLS) t-test. Our paper is the first of its kind in comparing the t-type tests for these different approaches to estimation. The results will be of value for applied statisticians and researchers.