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A note on the Hodges–Lehmann estimator
Author(s) -
Rosenkranz Gerd K.
Publication year - 2010
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.387
Subject(s) - wilcoxon signed rank test , estimator , mathematics , statistics , rank (graph theory) , parametric statistics , econometrics , combinatorics , mann–whitney u test
The Hodges‐Lehmann estimator was originally developed as a non‐parametric estimator of a shift parameter. As it is widely used in statistical applications, the question is investigated what it is estimating if the shift model does not hold. It is shown that for data whose distributions are symmetric about their median the Hodges–Lehmann estimator based on the Wilcoxon Rank Sum test estimates the difference between the medians of the distributions. This result does generally not hold if the symmetry assumption is violated. Copyright © 2009 John Wiley & Sons, Ltd.