An alternative approach to absolute-value test for the parameters of multiple linear regression models

Abstract

An alternative approach to absolute-value test statistic Mn is developed for conducting tests simultaneously on all the parameters of multiple linear regression models. Under certain null and alternative hypotheses, the new test statistic is shown to have limiting central and noncentral chisquare distributions, respectively. This paper uses a measure of efficiency due to Pitman to compare the asymptotic relative efficiency of the alternative approach to absolute-value test with its classical counterpart (the F-test). Numerical comparison of the alternative approach to absolute-value test with the F-test shows that the present test is slightly more efficient than the classical F-test for hni > 20 for all i, where hni = Σbjcji for all i. KEY WORDS: Alternative approach, absolute-value test, multiple linear regression models parameters, asymptotic relative efficiency. Global Journal of Mathematical Sciences Vol.3(2) 2004: 99-111