Non-null semi-parametric inference for the Mann - Whitney measure

Brown, B. M., Newcombe, Robert Gordon ORCID: https://orcid.org/0000-0003-4400-8867 and Zhao, Yudong 2009. Non-null semi-parametric inference for the Mann - Whitney measure. Journal of Nonparametric Statistics 21 (6) , pp. 743-755. 10.1080/10485250902999162

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Abstract

A simple method is introduced for finding large sample, boundary-respecting confidence intervals (CIs) for the two-sample Mann–Whitney measure, θ=Pr{X>Y}−Pr{X<Y}. This natural separation measure for two distributions occurs in stress–strength models, receiver operating characteristic curves, and nonparametrics generally. The usual estimate of θ is a centred version of the well-known Mann–Whitney statistic. Previous Wald-type CIs are not boundary-respecting. The difficulty is typically nonparametric, whereby appealing exact distributions hold only for one null parameter value, preventing the formulation of true distribution-free inference for non-null values. Here, the rank method setting and a result, that stochastic ordering is equivalent to monotone transformation of location shift, allow the assumption that data derive from a smooth location shift family. A suitable class of location shift families then model the asymptotic variance, leading to a rapidly converging iterative CI method based on roots of quadratics. Simulations show that the proposed method performs at least as well, or better, than competing CI methods.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Medicine
Subjects:	R Medicine > R Medicine (General)
Uncontrolled Keywords:	boundary-respecting confidence interval, extended logistic family, generalised hyperbolic secant distribution, location shift, stochastic ordering, AMS Subject Classification : 62G10, 62G15,
Publisher:	Taylor & Francis
ISSN:	1048-5252
Last Modified:	01 Nov 2022 10:56
URI:	https://orca.cardiff.ac.uk/id/eprint/93278

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