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

M. Hallin; T. Verdebout; Y. Swan

doi:10.1007/978-3-319-02651-0_9

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

M. Hallin, T. Verdebout, Y. Swan

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

2 Citations (Scopus)

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 language	English
Title of host publication	Contemporary Developments in Statistical Theory
Subtitle of host publication	Festschrift for Hira L. Koul
Editors	S.N. Lahiri, A. Schick, A. Sengupta, T.N. Sriram
Place of Publication	Heidelberg
Publisher	Springer Verlag
Pages	137-153
ISBN (Print)	9783319026503
DOIs	https://doi.org/10.1007/978-3-319-02651-0_9
Publication status	Published - 2014

Access to Document

10.1007/978-3-319-02651-0_9

Cite this

@inbook{113ae44dff6a413da962fffe6d7ae135,

title = "On Hodges and Lehmann's {"}6/pi result{"}",

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.",

author = "M. Hallin and T. Verdebout and Y. Swan",

year = "2014",

doi = "10.1007/978-3-319-02651-0_9",

language = "English",

isbn = "9783319026503",

pages = "137--153",

editor = "S.N. Lahiri and A. Schick and A. Sengupta and T.N. Sriram",

booktitle = "Contemporary Developments in Statistical Theory",

publisher = "Springer Verlag",

address = "Germany",

}

TY - CHAP

T1 - On Hodges and Lehmann's "6/pi result"

AU - Hallin, M.

AU - Verdebout, T.

AU - Swan, Y.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-319-02651-0_9

DO - 10.1007/978-3-319-02651-0_9

M3 - Chapter

SN - 9783319026503

SP - 137

EP - 153

BT - Contemporary Developments in Statistical Theory

A2 - Lahiri, S.N.

A2 - Schick, A.

A2 - Sengupta, A.

A2 - Sriram, T.N.

PB - Springer Verlag

CY - Heidelberg

ER -

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

Abstract

Access to Document

Fingerprint

Cite this