Statistical Methods & Applications

, Volume 20, Issue 4, pp 409–422 | Cite as

Robust nonparametric tests for the two-sample location problem

Article

Abstract

We construct and investigate robust nonparametric tests for the two-sample location problem. A test based on a suitable scaling of the median of the set of differences between the two samples, which is the Hodges-Lehmann shift estimator corresponding to the Wilcoxon two-sample rank test, leads to higher robustness against outliers than the Wilcoxon test itself, while preserving its efficiency under a broad range of distributions. The good performance of the constructed test is investigated under different distributions and outlier configurations and compared to alternatives like the two-sample t-, the Wilcoxon and the median test, as well as to tests based on the difference of the sample medians or the one-sample Hodges-Lehmann estimators.

Keywords

Distribution-free tests Wilcoxon test Outliers Heavy tails Skewed distributions 

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References

  1. Bandyopadhyay U, Dutta D (2010) Adaptive nonparametric tests for the two-sample scale problem under symmetry. Stat Methods Appl 19: 153–170MathSciNetCrossRefGoogle Scholar
  2. Bovik AC, Munson DC Jr (1986) Edge detection using median comparisons. Comput Vision Graph Image Process 33: 377–389CrossRefGoogle Scholar
  3. Edgington ES (1995) Randomization tests. 3rd. Marcel Dekker, New YorkMATHGoogle Scholar
  4. Fried R (2007) On robust shift detection in time series. Comput Stat Data Anal 52: 1063–1074MATHCrossRefGoogle Scholar
  5. Fried R (2011) On the online estimation of piecewise constant volatilities. Comput Stat Data Anal, (in press). doi:10.1016/j.csda.2011.02.012
  6. Hodges JL, Lehmann EL (1963) Estimates of location based on rank tests. Ann Math Stat 34: 598–611MathSciNetMATHCrossRefGoogle Scholar
  7. Hoyland A (1965) Robustness of the Hodges-Lehmann estimates for shift. Ann Math Stat 36: 174–197MathSciNetMATHCrossRefGoogle Scholar
  8. Keselman HJ, Wilcox RR, Kowalchuk RK, Olejnik S (2002) Comparing trimmed or least squares means of two independent skewed populations. Biom J 44: 478–489MathSciNetCrossRefGoogle Scholar
  9. Lehmann EL (1963a) Robust estimation in analysis of variance. Ann Math Stat 34: 957–966MathSciNetMATHCrossRefGoogle Scholar
  10. Lehmann EL (1963b) Asymptotically nonparametric inference: an alternative approach to linear models. Ann Math Stat 34: 1494–1506MathSciNetMATHCrossRefGoogle Scholar
  11. Lehmann EL (1963c) Nonparametric confidence intervals for a shift parameter. Ann Math Stat 34: 1507–1512MathSciNetMATHCrossRefGoogle Scholar
  12. Mathur SK (2009) A new nonparametric bivariate test for two sample location problem. Stat Methods Appl 18: 375–388MathSciNetCrossRefGoogle Scholar
  13. Morgenthaler S (2007) A survey of robust statistics (with discussion). Stat Methods Appl 15: 271–293MathSciNetCrossRefGoogle Scholar
  14. Reed JF III, Stark (2004) Robust two-sample statistics for equality of means: a simulation study. J Appl Stat 31: 831–854MathSciNetMATHCrossRefGoogle Scholar
  15. R Development Core Team (2009) R: A language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.R-project.org
  16. Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New YorkMATHCrossRefGoogle Scholar
  17. Simonoff JS (1996) Smoothing methods in Statistics. Springer, New YorkMATHCrossRefGoogle Scholar
  18. Wilcox RR, Keselman HJ (2003) Modern robust data analysis methods: measures of central tendency. Psychol Methods 8: 254–274CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of StatisticsTU Dortmund UniversityDortmundGermany
  2. 2.Department of MathematicsRuhr-University of BochumBochumGermany

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