A unified approach to the asymptotic distribution theory of certain midrank statistics

  • F. H. Ruymgaart
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 821)


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  1. [1]
    BEHNEN, K. (1973). Asymptotic properties of averaged scores rank tests of independence. Proc. of the Prague Symp. on Asymptotic Statist. (Hájek ed.), Vol.II, 5–30.MathSciNetGoogle Scholar
  2. [2]
    BEHNEN, K. (1976). Asymptotic comparison of rank tests for the regression problem when ties are present. Ann. Statist. 4, 157–174.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    BEHNEN, K. (1978). Vorzeichen-Rangtests mit Nullen und Bindungen. Tech. Report 13, Dept. Mathematics Un. Bremen.Google Scholar
  4. [4]
    CHERNOFF, H. and SAVAGE, I.R. (1958). Asymptotic normality and efficiency of certain nonparametric test statistics. Ann. Math. Statist. 29, 972–994.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    CONOVER, W.J. (1973). Rank tests for one sample, two samples and k samples without the assumption of a continuous distribution function. Ann. Statist. 1, 1105–1125.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    HÁJEK, J. (1969). A Course in Nonparametric Statistics. Holden-Day, San Francisco.zbMATHGoogle Scholar
  7. [7]
    MOORE, D.S. (1968). An elementary proof of asymptotic normality of linear functions of order statistics. Ann. Math. Statist. 39, 263–265.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    RUYMGAART, F.H. (1979). Asymptotic theory of a class of midrank statistics in the non-i.i.d. case. Tech. Report 7909, Dept. of Mathematics Cath.Un. Nijmegen.Google Scholar
  9. [9]
    RUYMGAART, F.H. and ZUIJLEN, M.C.A. van (1977). Asymptotic normality of linear combinations of functions of order statistics in the non-i.i.d.-case. Indag.Math. 80, 432–447.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    RUYMGAART, F.H. and ZUIJLEN, M.C.A. van (1978). Asymptotic normality of multivariate linear rank statistics in the non-i.i.d. case. Ann. Statist. 6, 588–602.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    VORLICKOVÁ, D. (1970). Asymptotic properties of rank tests under discrete distributions. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 14, 275–289.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    VORLICKOVÁ, D. (1972). Asymptotic properties of rank tests of symmetry under discrete distributions. Ann. Math. Statist. 43, 2013–2018.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    ZUIJLEN, M.C.A. van (1978). Properties of the empirical distribution function for independent non-identically distributed random variables. Ann. Probability 6, 250–266.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • F. H. Ruymgaart
    • 1
  1. 1.Department of MathematicsKatholieke Un. Nijmegen ToernooiveldNijmegenThe Netherlands

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