A JONCKHEERE TYPE TEST FOR THE PARALLELISM OF REGRESSION LINES
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this paper, we propose a Jonckheere type test statistic for testing the parallelism of k regression lines against ordered alternatives. The order restriction problems could arise in various settings such as location, scale, and regression problems. But most of theory about the statistical inferences under restrictions has been developed to deal with location parameters. The proposed test is an application of Jonckheere's procedure to regression problem. Asymptotyic normality and asynptotic distribution-free properties of the test statistic are obtained under some regularity conditions.
Abstract
In this paper, we propose a Jonckheere type test statistic for testing the parallelism of k regression lines against ordered alternatives. The order restriction problems could arise in various settings such as location, scale, and regression problems. But most of theory about the statistical inferences under restrictions has been developed to deal with location parameters. The proposed test is an application of Jonckheere's procedure to regression problem. Asymptotyic normality and asynptotic distribution-free properties of the test statistic are obtained under some regularity conditions.
참고문헌 (8)
- J.N. Adichie, "Testing Parallelism of Regression Lines against Ordered Alternatives", Communications in Statistics, Theory and Mathematics, A5(11), pp.985~997 (1976)
- E.S. Jee, "A Study on a Nonparametric Test for the Parallelism of k Regression Lines Against Ordered Alternatives", J. Appl. Math. & Computing, 8, pp.669~682 (2001)
- E.S. Jee, "A Study on a Nonparametric Test with Regression Depth", Journal of Institute of Statistics Korea University, 20, pp.65~76 (2005)
- A.R. Jonckheere, "A Distribution-free k-sample Test Against Ordered Alternatives", Biometrika, 41, pp.133~145 (1954)
- J.L. Kepner, "A Distribution-free Rank Test for Ordered Alternatives in Randomized Complete Block Designs", Journal of American Statistical Association, 79, pp.212~217 (1984)
- R.H. Randles, "On Tests Applied to Residuals", Journal of American Statistical Associ-ation, 79, pp.349~354 (1984)
- K.S.M. Rao, "Testing Concurrence and Parallelism of Several Sample Regressions Against Ordered Alternatives", U. Stat. Ser. Statist, 15, pp.43~50 (1984)
- M.S. Song, "On a Distribution-free Test for Parallelism of Regression Lines Against Ordered Alternatives", Journal of Korean Society for Quality Control, 15(2), pp.50~54 (1987)