Skip to main content
SpringerLink
Log in

Asymptotic Efficiency of Maesono Statistics for Testing of Symmetry

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In an interesting paper Maesono introduced a new class of distribution-free statistics for testing of symmetry against shift alternative. The simplest of them coincides with the Wilcoxon statistic while the next is different but has the same Pitman efficiency. Maesono raised the problem of comparison between these two statistics on the basis of exact Bahadur efficiency. In this paper we calculate exact local Bahadur indices for all Maesono statistics and show when his statistics are better than the Wilcoxon statistic for sufficiently close alternatives.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bahadur, R. R. (1960). Stochastic comparison of tests, Ann. Math. Statist., 31(2), 276–295.

    Google Scholar 

  • Bahadur, R. R. (1971). Some Limit Theorems in Statistics, Siam, Philadelphia.

  • Dasgupta, R. (1984). On large deviation probabilities of U-statistics in non-i.i.d. case, Sankhyā Ser. A, 46(1), 110–116.

    Google Scholar 

  • Maesono, Y. (1987). Competitors of the Wilcoxon Signed Rank Test, Ann. Inst. Statist. Math., 39, 363–375.

    Google Scholar 

  • Nikitin, Ya. Yu. (1995). Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press, New York.

    Google Scholar 

  • Nikitin, Ya. Yu. and Ponikarov, E. V. (1998). On Chernoff type large deviations for U-and V-statistics, Asymptotic Methods in Probability and Mathematical Statistics, Abstracts of Communications of International Conference, St. Petersburg, June 24–28, 1998, 226–228.

  • Nikitin, Ya. Yu. and Ponikarov, E. V. (1999a). Rough large deviation asymptotics of Chernoff type for von Mises functionals and U-statistics, Proceedings of St. Petersburg Mathematical Society, 1999, Vol. 7, 124–167 (English translation (2001), Amer. Math. Soc. Trans. Ser. 2, 203, 107–146).

    Google Scholar 

  • Nikitin, Ya. Yu. and Ponikarov, E. V. (1999b). Large deviations of Chernoff type for U-and V-statistics, Doklady Russian Academy of Sciences, 369(1), 10–12.

    Google Scholar 

  • Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, St. Petersburg State University, 198504, Petrodvorets, Russian Federation

    Ya. Yu. Nikitin & E. V. Ponikarov

Authors
  1. Ya. Yu. Nikitin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Ponikarov
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Nikitin, Y.Y., Ponikarov, E.V. Asymptotic Efficiency of Maesono Statistics for Testing of Symmetry. Annals of the Institute of Statistical Mathematics 54, 382–390 (2002). https://doi.org/10.1023/A:1022482220794

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022482220794

Search

Navigation