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Kruskal-Wallis one-way analysis of variance based on linear placements

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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.

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.

참고문헌 (11)

  1. H. Chernoff, "Asymptotic normality and efficiency of certain nonpara-metric test statistics", Ann. Math. Statist, 29, pp.972~994 (1958)
  2. V. Dupac, "Asymptotic normality of simple linear rank statistics under alternative II", Ann. Math. Statist, 40, pp.1992~2017 (1969)
  3. Z. Govindarajulu, "Generalizations of theorems of Chernoff and Savage on the asymptotic normality of test statistics", Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, pp.609~638 (1967), Univ. California Press
  4. J. Hajek, "Asymptotic normality of simple linear rank statistics under alternatives", Ann. Math. Statist, 39, pp.325~346 (1968)
  5. D. Kim, "A class of distribution-free treatments versus control tests based on placements,", Far East J. Theor. Stat, 3(1), pp.19~33 (1999)
  6. D. Kim, "The asymptotic behavior of linear placement statistics", Statist. Probab. Lett, 81(2), pp.326~336 (2011)
  7. D. Kim, "Properties of distribution-free two-sample procedures based on placements", Far East J. Math. Sci, 1(2), pp.179~190 (1993)
  8. A. M. Mood, "Introduction to the Theory of Statistics" (1950), McGraw-Hill
  9. J. Orban, "A class of distribution-free two-sample tests based on place-ments", J. Amer. Statist. Assoc, 77(379), pp.666~672 (1982)
  10. R. Pyke, "Weak convergence of a two-sample empirical process and a new approach to Chernoff-Savage theorems", Ann. Math. Statist, 39, pp.755~771 (1968)
  11. F. Wilcoxon, "Individual comparisons by ranking methods", Biometrics, 1(6), pp.80~83 (1945)

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