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

M. Hallin, T. Verdebout, Y. Swan

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

    1 Citation (Scopus)


    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
    ISBN (Print)9783319026503
    Publication statusPublished - 2014


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