A JONCKHEERE TYPE TEST FOR THE PARALLELISM OF REGRESSION LINES

Abstract. In this paper, we propose a Jonckheere type test statistic for testing the parallelism of k regression lines against ordered alternatives. The order restric-tion problems could arise in various settings such as location, scale, and regression problems. But most of theory about the statistical inferences under order restric-tions has been developed to deal with location parameters. The proposed test is an application of Jonckheere’s procedure to regression problem. Asymptotic normality and asymptotic distribution-free properties of the test statistic are obtained under some regularity conditions. 1