On Some Test Statistics for Coefficients in the Ridge, Liu and Kibria–Lukman Linear Regression Models: A Simulation Study

Ridge, Liu, and Kibria–Lukman regression methods that have been proposed to solve the multicollinearity problem for both linear and generalized linear regression models (Kibria and Lukman, Shewa and Ugwuowo). This paper considers several different ridge, Liu, and Kibria–Lukman regression t-type tests of the individual coefficients in a linear regression model. A simulation study has been conducted to evaluate and compare the performance of the tests with respect to their empirical size and power under different conditions, such as level of correlation in the data, correlation structure, sample size, and number of covariates in the model. Simulation results allowed us to identify among the proposed tests, which ones maintain 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. This paper will be the first of its kind in putting together and comparing the t-type tests for these different approaches. The findings of this research contribute to statistical methodology by offering practical guidance on selecting shrinkage estimators in the presence of multicollinearity, thereby improving decision-making in linear regression models.