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KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BASED ON LINEAR PLACEMENTS

  • Hong, Yicheng (Department of Mathematics Yanbian University) ;
  • Lee, Sungchul (Department of Mathematics Yanbian University)
  • Received : 2013.03.01
  • Published : 2014.05.31

Abstract

The limiting distribution for the linear placement statistics under the null hypotheses has been provided by Orban and Wolfe [9] and Kim [5] when one of the sample sizes goes to infinity, and by Kim, Lee and Wang [6] when the sample sizes of each group go to infinity simultaneously. In this paper we establish the generalized Kruskal-Wallis one-way analysis of variance for the linear placement statistics.

Keywords

Kruskal-Wallis one-way analysis of variance;central limit theorem;linear placement statistic

References

  1. J. Hajek, Asymptotic normality of simple linear rank statistics under alternatives, Ann. Math. Statist. 39 (1968), 325-346. https://doi.org/10.1214/aoms/1177698394
  2. H. Chernoff and I. R. Savage, Asymptotic normality and efficiency of certain nonparametric test statistics, Ann. Math. Statist. 29 (1958), 972-994. https://doi.org/10.1214/aoms/1177706436
  3. V. Dupac and J. Hajek, Asymptotic normality of simple linear rank statistics under alternative II., Ann. Math. Statist. 40 (1969), 1992-2017. https://doi.org/10.1214/aoms/1177697281
  4. Z. Govindarajulu, L. Le Cam, and M. Raghavachari, Generalizations of theorems of Chernoff and Savage on the asymptotic normality of test statistics, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Vol. I: Statistics, pp. 609-638 Univ. California Press, Berkeley, Calif, 1967.
  5. D. Kim, A class of distribution-free treatments versus control tests based on placements, Far East J. Theor. Stat. 3 (1999), no. 1, 19-33.
  6. D. Kim, S. Lee, and W. Wang, The asymptotic behavior of linear placement statistics, Statist. Probab. Lett. 81 (2011), no. 2, 326-336. https://doi.org/10.1016/j.spl.2010.10.021
  7. D. Kim and D. A. Wolfe, Properties of distribution-free two-sample procedures based on placements, Far East J. Math. Sci. 1 (1993), no. 2, 179-190.
  8. A. M. Mood, Introduction to the Theory of Statistics, McGraw-Hill, New York, 1950.
  9. J. Orban and D. A. Wolfe, A class of distribution-free two-sample tests based on placements, J. Amer. Statist. Assoc. 77 (1982), no. 379, 666-672. https://doi.org/10.1080/01621459.1982.10477870
  10. R. Pyke and G. R. Shorack, Weak convergence of a two-sample empirical process and a new approach to Chernoff-Savage theorems, Ann. Math. Statist. 39 (1968), 755-771. https://doi.org/10.1214/aoms/1177698309
  11. F. Wilcoxon, Individual comparisons by ranking methods, Biometrics 1 (1945), no. 6, 80-83. https://doi.org/10.2307/3001968

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