The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

A JONCKHEERE TYPE TEST FOR THE PARALLELISM OF REGRESSION LINES

  • Received : 2013.02.08
  • Accepted : 2013.04.30
  • Published : 2013.05.31
Download PDF
⟨ Previous Next ⟩

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 order restrictions 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.

Keywords

Acknowledgement

Supported by : Kwangwoon University

References

  1. J.N. Adichie: Testing Parallelism of Regression Lines against Ordered Alternatives. Communications in Statistics, Theory and Mathematics A5 (1976), no. 11, 985-997.
  2. E.S. Jee: A Study on a Nonparametric Test for the Parallelism of k Regression Lines Against Ordered Alternatives. J. Appl. Math. & Computing 8 (2001), 669-682.
  3. E.S. Jee: A Study on a Nonparametric Test with Regression Depth, Journal of Institute of Statistics Korea University 20 (2005), 65-76.
  4. A.R. Jonckheere: A Distribution-free k-sample Test Against Ordered Alternatives. Biometrika 41 (1954), 133-145. https://doi.org/10.1093/biomet/41.1-2.133
  5. J.L. Kepner & D.H. Robinson: A Distribution-free Rank Test for Ordered Alternatives in Randomized Complete Block Designs. Journal of American Statistical Association 79 (1984), 212-217. https://doi.org/10.1080/01621459.1984.10477087
  6. R.H. Randles: On Tests Applied to Residuals. Journal of American Statistical Association 79 (1984), 349-354. https://doi.org/10.1080/01621459.1984.10478056
  7. K.S.M. Rao & A.P. Gore: Testing Concurrence and Parallelism of Several Sample Regressions Against Ordered Alternatives. U. Stat. Ser. Statist. 15 (1984), 43-50. https://doi.org/10.1080/02331888408801745
  8. M.S. Song, M.Y. Huh & H.J. Kang: On a Distribution-free Test for Parallelism of Regression Lines Against Ordered Alternatives. Journal of Korean Society for Quality Control 15 (1987), no. 2, 50-54.

Cited by

  1. 여러 개의 단순선형회귀모형에서 순차기울기를 이용한 평행성 검정 vol.29, pp.4, 2013, https://doi.org/10.7465/jkdi.2018.29.4.873