Empirical likelihood ratio based comparative study on tests for normality of residuals in linear models

Abstract

The application of goodness-of-fit (GoF) tests in linear regression modeling is a common practice in applied statistical sciences. For instance, in simple linear regression the assumption of normality of residuals is always necessary to test before making any further inferences. The growing popularity of the use of powerful and efficient empirical likelihood ratio (ELR) based GoF tests in checking for departures from normality in various continuous distributions can be of great use in checking for distributional assumptions of residuals in linear models. Motivated by the attractive properties of the ELR based GoF tests the researchers conducted an extensive Type I error rate assessment as well as a Monte Carlo power comparison of selected ELR GoF tests with well-known existing tests against symmetric and asymmetric alternative OLS and BLUS residuals. Under the simulated scenarios, all the studied tests have good control of Type I error rates. The Monte Carlo experiments revealed the superiority of the ELR GoF tests under certain alternatives of both the OLS and BLUS residuals. Our findings also demonstrated the superiority of OLS over BLUS residuals when one is testing for normality in simple linear regression models. A real data study further revealed the applicability of the ELR based GoF tests in testing normality of residuals in linear regression models.