### Abstract

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 | |

Publication status | Published - 2014 |

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### Cite this

*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

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*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.

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

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 -