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A class of outlier resistant two-sample scale tests

Author Affiliations

  • 1Dept. of Statistics, Karnatak University, Dharwad, Karnataka, India
  • 2Dept. of Statistics, Karnatak University, Dharwad, Karnataka, India

Res. J. Mathematical & Statistical Sci., Volume 8, Issue (1), Pages 6-15, January,12 (2020)

Abstract

A class of two-sample scale tests which is resistant to outliers of one sample is suggested. The tests are distribution-free tests based on U-statistics being functions of median and extremes of subsamples respectively drawn from first and second samples. The null and asymptotic distributions of the class of tests are obtained. The asymptotic relative efficiencies of some members of the class with respect to various tests are calculated to analyze the large sample performance. Empirical power of the proposed class of tests for various sample and subsample sizes under various distributions is computed to investigate the small sample performance.

References

  1. Fisher R.A. (1924)., On a distribution yielding the error functions of several well known statistics., Proceedings of International Congress of Mathematicians, Toronto 2, 805-813.
  2. Wilcoxon F. (1945)., Individual comparisons by ranking methods., Biometrics Bull., 1, 80-83.
  3. Mann H.B. and Whitney D.R. (1947)., On a test of whether one of two random variables is stochastically larger than the other., Ann. Math. Statist., 18(1), 50-60.
  4. Lehmann E.L. (1951)., Consistency and Unbiasedness of certain nonparametric tests., Ann. Math. Statist., 22, 165-179.
  5. Mood A.M. (1954)., On the asymptotic efficiency of certain nonparametric two-sample tests., Ann. Math. Statist., 25, 514-522.
  6. Sukhatme B.V. (1957)., On certain two-sample nonparametric tests for variances., Ann. Math. Statist., 28, 188-194.
  7. Sukhatme B.V. (1958)., A two-sample distribution-free test for comparing variances., Biometrika, 45, 544-548.
  8. Deshpande J.V. and Kusum K. (1984)., A test for nonparametric two-sample scale problem., Aust. Jour. Stat., 26, 16-24.
  9. Kusum K. (1985)., A new distribution-free test for two-sample scale problem., Jour. Indi. Stat. Assoc., 23, 97-107.
  10. Shetty I.D. and Pandit P.V. (2004)., A note on a new class of distribution-free tests for the two sample scale problem based on subsample medians., Comm. Statist. Theory and Methods., 33(9), 2271-2280.
  11. Bhat S.V., Shindhe S.D. and Joshi V.B. (2018)., A Class of outlier resistant tests for two-sample scale problem., Int. J. Agricult. Stat. Sci., 14(2), 455-463.
  12. Bhat S.V. and Shindhe S.D. (2019)., Distribution-free tests based on subsample maxima or minima for two-sample scale problem., Bull. Math. &Stat. Res., 7(3), 20-35.
  13. Bhat S.V. and Shindhe S.D. (2019)., A class of two-sample scale tests based on U-statistics., International Journal of Research- Granthalayah, 7(9), 138-147.
  14. Bhat S.V. (1995)., Studies in Nonparametric Inference., An unpublished Ph.D. thesis submitted to the Karnatak University, Dharwad.
  15. Siegel S. and Tukey J.W. (1960)., A nonparametric sum of ranks procedure for relative spread in unpaired samples., Jour. Amer. Statist. Assoc., 55, 429-445.
  16. Shetty I.D. and Bhat S.V. (1993)., A class of distribution-free tests for the two-sample scale problem., Proceedings of II International symposium on Optimization and Statistics, Aligarh, India, Nov 2-4, 91-96.
  17. Deshpande J.V., Gore A.P. and Shanubhogue A. (1995)., Statistical analysis of Nonnormal data., New Age International Publishers Limited, Wiley Eastern Limited. ISBN: 81-224-0707-2.