The robustness against dependence of nonparametric tests for the two-sample location problem

Przemysław Grzegorzewski

Applicationes Mathematicae (1995)

  • Volume: 22, Issue: 4, page 469-476
  • ISSN: 1233-7234

Abstract

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Nonparametric tests for the two-sample location problem are investigated. It is shown that the supremum of the size of any test can be arbitrarily close to 1. None of these tests is most robust against dependence.

How to cite

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Grzegorzewski, Przemysław. "The robustness against dependence of nonparametric tests for the two-sample location problem." Applicationes Mathematicae 22.4 (1995): 469-476. <http://eudml.org/doc/219107>.

@article{Grzegorzewski1995,
abstract = {Nonparametric tests for the two-sample location problem are investigated. It is shown that the supremum of the size of any test can be arbitrarily close to 1. None of these tests is most robust against dependence.},
author = {Grzegorzewski, Przemysław},
journal = {Applicationes Mathematicae},
keywords = {size of test; robustness of tests; nonparametric tests for the two-sample location problem; robustness against dependence; Rueschendorf's epsilon neighbourhoods; Mann-Whitney- Wilcoxon test; two-sample location problem},
language = {eng},
number = {4},
pages = {469-476},
title = {The robustness against dependence of nonparametric tests for the two-sample location problem},
url = {http://eudml.org/doc/219107},
volume = {22},
year = {1995},
}

TY - JOUR
AU - Grzegorzewski, Przemysław
TI - The robustness against dependence of nonparametric tests for the two-sample location problem
JO - Applicationes Mathematicae
PY - 1995
VL - 22
IS - 4
SP - 469
EP - 476
AB - Nonparametric tests for the two-sample location problem are investigated. It is shown that the supremum of the size of any test can be arbitrarily close to 1. None of these tests is most robust against dependence.
LA - eng
KW - size of test; robustness of tests; nonparametric tests for the two-sample location problem; robustness against dependence; Rueschendorf's epsilon neighbourhoods; Mann-Whitney- Wilcoxon test; two-sample location problem
UR - http://eudml.org/doc/219107
ER -

References

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  1. [1] P. Grzegorzewski, Nonparametric tests for two-sample location problem, Mat. Stos. 34 (1991), 37-57 (in Polish). Zbl0752.62037
  2. [2] P. Grzegorzewski, The infinitesimal robustness of tests against dependence, Zastos. Mat. 21 (3) (1992), 455-460. Zbl0782.62052
  3. [3] M. Hollander, G. Pledger and P. E. Lin, Robustness of the Wilcoxon test to a certain dependency between samples, Ann. Statist. 2 (1974), 177-181. Zbl0273.62025
  4. [4] A. N. Pettit and V. Siskind, Effect of within-sample dependence on the MWW statistic, Biometrica 68 (1981), 437-441. Zbl0465.62024
  5. [5] L. Rüschendorf, Construction of multivariate distributions with given marginals, Ann. Inst. Statist. Math. 37 (1985), 225-233. Zbl0573.62045
  6. [6] R. J. Serfling, The Wilcoxon two-sample statistic on strongly mixing processes, Ann. Math. Statist. 39 (1968), 1202-1209. Zbl0162.21905
  7. [7] R. Zieliński, Robust statistical procedures: a general approach, in: Lecture Notes in Math. 982, Springer, 1983, 283-295. 
  8. [8] R. Zieliński, Robustness of two-sample tests to dependence of the observations, Mat. Stos. 32 (1989), 5-18 (in Polish). Zbl0714.62042
  9. [9] R. Zieliński, Robustness of the one-sided Mann-Whitney-Wilcoxon test to dependency between samples, Statist. Probab. Lett. 10 (1990), 291-295. Zbl0703.62059

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