Skip to main content
Log in

Efficiency comparison of the Wilcoxon tests in paired and independent survey samples

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

The efficiency concepts of Bahadur and Pitman are used to compare the Wilcoxon tests in paired and independent survey samples. A comparison through the length of corresponding confidence intervals is also done. Simple conditions characterizing the dominance of a procedure are derived. Statistical tests for checking these conditions are suggested and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Bahadur RR (1971) Some limit theorems in statistics. SIAM, Philadelphia

    Book  Google Scholar 

  • Baringhaus L, Gaigall D (2017) Hotelling’s \(T^2\) tests in paired and independent survey samples—an efficiency comparison. J Multivar Anal 154:177–198

    Article  Google Scholar 

  • Callaert H, Veraverbeke N (1981) The order of the normal approximation for a studentized \(U\)-statistic. Ann Stat 9:194–200

    Article  MathSciNet  Google Scholar 

  • Gibbons JD, Chakraborti S (2011) Nonparametric statistical inference. CRC Press, Boca Raton

    Book  Google Scholar 

  • Groeneboom P, Oosterhoff J (1977) Bahadur efficiency and probabilities of large deviations. Stat Neerl 31:1–24

    Article  MathSciNet  Google Scholar 

  • Hájek J, Šidak Z, Sen PK (1999) Theory of rank tests. Academic Press, San Diego

    Chapter  Google Scholar 

  • Hettmansperger TP (1984) Statistical inference based on ranks. Wiley, New York

    MATH  Google Scholar 

  • Hodges JL, Lehmann EL (1956) The efficiency of some nonparametric competitors of the \(t\)-test. Ann Math Stat 27:324–335

    Article  MathSciNet  Google Scholar 

  • Hoeffding W (1940) Maßstabinvariante Korrelationstheorie. Schriften des Mathematischen Institiuts und des Instituts für Angewandte Mathematik der Universität Berlin 5:179–233

  • Hollander M (1967) Asymptotic efficiency of two nonparametric competitors of Wilcoxon’s two-sample test. J Am Stat Assoc 62:939–949

    Article  MathSciNet  Google Scholar 

  • Jammalamadaka SR, Janson S (1986) Limit theorems for a triangular scheme of \(U\)-statistics with applications to inter-point distances. Ann Probab 14:1347–1358

    Article  MathSciNet  Google Scholar 

  • Nikitin Y (1995) Asymptotic efficiency of nonparametric tests. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Nikitin Y, Ponikarov E (2001) Rough asymptotics of probabilities of Chernoff type large deviations for von Mises functionals and \(U\)-statistics. Am Math Soc Transl 203:107–146

    MathSciNet  MATH  Google Scholar 

  • Pratt J (1961) Length of confidence intervals. J Am Stat Assoc 56:549–567

    Article  MathSciNet  Google Scholar 

  • Serfling RS (1980) Approximation theorems of mathematical statistics. Wiley, New York

    Book  Google Scholar 

  • Shirahata S, Sakamoto Y (1992) Estimate of variance of U-statistics. Commun Stat Theory Methods 10:2969–2981

    Article  Google Scholar 

  • Weber NC (1980) Rates of convergence for U-statistics with varying kernels. Bull Austral Math Soc 21:1–5

    Article  MathSciNet  Google Scholar 

  • Wieand HS (1976) A condition under which the Pitman and Bahadur approaches to efficiency coincide. Ann Stat 4:1003–1011

    Article  MathSciNet  Google Scholar 

  • Witting H, Müller-Funk U (1995) Mathematische Statistik II. Teubner, Stuttgart

    Book  Google Scholar 

Download references

Acknowledgements

The authors thank the editor and the referees for constructive comments and suggestions. The second author was supported by a doctoral scholarship from the Hans-Böckler-Stiftung.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel Gaigall.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baringhaus, L., Gaigall, D. Efficiency comparison of the Wilcoxon tests in paired and independent survey samples. Metrika 81, 891–930 (2018). https://doi.org/10.1007/s00184-018-0661-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-018-0661-4

Keywords

Mathematics Subject Classification

Navigation