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Asymptotic behavior of functionals of empirical distribution functions for the two-sample problem

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Summary

Mises functional is extended for the two-sample problem. It is shown that the extended Mises functional also has the asymptotic property given by von Mises (1947,Ann. Math. Statist.,18, 309–348) and by Filippova (1962,Theory Prob. Appl.,7, 24–57) in the one-sample case. Asymptotic behavior ofU-statistic in the two-sample case, the statistic of Cramér-von Mises type for testing homogeneity and so forth are investigated as important examples of the theory.

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References

  1. Aki, S. (1981). Asymptotic distribution of a Cramér-von Mises type statistic for testing symmetry when the center is estimated,Ann. Inst. Statist. Math.,33, A, 1–14.

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  2. Billingsley, P. (1968).Convergence of Probability Measures, John Wiley & Sons.

  3. Filippova, A. A. (1962). Mises' theorem of the asymptotic behavior of functionals of empirical distribution functions and its statistical applications,Theory Prob. Appl.,7, 24–57.

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  4. Fisz, M. (1960). On a result by M. Rosenblatt concerning the von Mises-Smirnov test,Ann. Math. Statist.,31, 427–429.

    Article  MathSciNet  Google Scholar 

  5. Lehmann, E. L. (1951). Consistency and unbiasedness of certain nonparametric tests,Ann. Math. Statist.,22, 165–179.

    Article  MathSciNet  Google Scholar 

  6. Rosenblatt, M. (1952). Limit theorems associated with variants of the von Mises statistics,Ann. Math. Statist.,23, 617–623.

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  7. von Mises, R. (1947). On the asymptotic distribution of differentiable statistical functions,Ann. Math. Statist.,18, 309–348.

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Authors
  1. Sigeo Aki
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The Institute of Statistical Mathematics

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Aki, S. Asymptotic behavior of functionals of empirical distribution functions for the two-sample problem. Ann Inst Stat Math 33, 391–403 (1981). https://doi.org/10.1007/BF02480950

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  • DOI: https://doi.org/10.1007/BF02480950

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