On Hodges and Lehmann's "6/pi result"

M. Hallin, T. Verdebout, Y. Swan

    Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

    Abstract

    While the asymptotic relative efficiency (ARE) of Wilcoxon rank-based tests for location and regression with respect to their parametric Student competitors can be arbitrarily large, Hodges and Lehmann (1961) have shown that the ARE of the same Wilcoxon tests with respect to their van der Waerden or normal-score counterparts is bounded from above by 6/π≈1.910. In this chapter, we revisit that result, and investigate similar bounds for statistics based on Student scores. We also consider the serial version of this ARE. More precisely, we study the ARE, under various densities, of the Spearman–Wald–Wolfowitz and Kendall rank-based autocorrelations with respect to the van der Waerden or normal-score ones used to test (ARMA) serial dependence alternatives.
    Original languageEnglish
    Title of host publicationContemporary Developments in Statistical Theory
    Subtitle of host publicationFestschrift for Hira L. Koul
    EditorsS.N. Lahiri, A. Schick, A. Sengupta, T.N. Sriram
    Place of PublicationHeidelberg
    PublisherSpringer Verlag
    Pages137-153
    ISBN (Print)9783319026503
    DOIs
    Publication statusPublished - 2014

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    Asymptotic Relative Efficiency
    Pi
    Serial Dependence
    Wilcoxon Test
    Autoregressive Moving Average
    Autocorrelation
    Regression
    Statistics
    Alternatives

    Cite this

    Hallin, M., Verdebout, T., & Swan, Y. (2014). On Hodges and Lehmann's "6/pi result". In S. N. Lahiri, A. Schick, A. Sengupta, & T. N. Sriram (Eds.), Contemporary Developments in Statistical Theory: Festschrift for Hira L. Koul (pp. 137-153). Heidelberg: Springer Verlag. https://doi.org/10.1007/978-3-319-02651-0_9
    Hallin, M. ; Verdebout, T. ; Swan, Y. / On Hodges and Lehmann's "6/pi result". Contemporary Developments in Statistical Theory: Festschrift for Hira L. Koul. editor / S.N. Lahiri ; A. Schick ; A. Sengupta ; T.N. Sriram. Heidelberg : Springer Verlag, 2014. pp. 137-153
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    abstract = "While the asymptotic relative efficiency (ARE) of Wilcoxon rank-based tests for location and regression with respect to their parametric Student competitors can be arbitrarily large, Hodges and Lehmann (1961) have shown that the ARE of the same Wilcoxon tests with respect to their van der Waerden or normal-score counterparts is bounded from above by 6/π≈1.910. In this chapter, we revisit that result, and investigate similar bounds for statistics based on Student scores. We also consider the serial version of this ARE. More precisely, we study the ARE, under various densities, of the Spearman–Wald–Wolfowitz and Kendall rank-based autocorrelations with respect to the van der Waerden or normal-score ones used to test (ARMA) serial dependence alternatives.",
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    Hallin, M, Verdebout, T & Swan, Y 2014, On Hodges and Lehmann's "6/pi result". in SN Lahiri, A Schick, A Sengupta & TN Sriram (eds), Contemporary Developments in Statistical Theory: Festschrift for Hira L. Koul. Springer Verlag, Heidelberg, pp. 137-153. https://doi.org/10.1007/978-3-319-02651-0_9

    On Hodges and Lehmann's "6/pi result". / Hallin, M.; Verdebout, T.; Swan, Y.

    Contemporary Developments in Statistical Theory: Festschrift for Hira L. Koul. ed. / S.N. Lahiri; A. Schick; A. Sengupta; T.N. Sriram. Heidelberg : Springer Verlag, 2014. p. 137-153.

    Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

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    Hallin M, Verdebout T, Swan Y. On Hodges and Lehmann's "6/pi result". In Lahiri SN, Schick A, Sengupta A, Sriram TN, editors, Contemporary Developments in Statistical Theory: Festschrift for Hira L. Koul. Heidelberg: Springer Verlag. 2014. p. 137-153 https://doi.org/10.1007/978-3-319-02651-0_9