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
|
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: | 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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