 Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validationL. Baringhaus and N. Henze Journal of Nonparametric Statistics, 2017, vol. 29, issue 2, 167-188 Abstract: We give a probabilistic interpretation of the Cramér–von Mises distance $ \Delta (F,F_0) = \int (F-F_0)^2\,{\rm d}F_0 $ Δ(F,F0)=∫(F−F0)2dF0 between continuous distribution functions F and $ F_0 $ F0. If F is unknown, we construct an asymptotic confidence interval for $ \Delta (F,F_0) $ Δ(F,F0) based on a random sample from F. Moreover, for given $ F_0 $ F0 and some value $ \Delta _0>0 $ Δ0>0, we propose an asymptotic equivalence test of the hypothesis that $ \Delta (F,F_0) \ge \Delta _0 $ Δ(F,F0)≥Δ0 against the alternative $ \Delta (F,F_0) < \Delta _0 $ Δ(F,F0)<Δ0. If such a ‘neighbourhood-of- $ F_0 $ F0 validation test’, carried out at a small asymptotic level, rejects the hypothesis, there is evidence that F is within a distance $ \Delta _0 $ Δ0 of $ F_0 $ F0. As a neighbourhood-of-exponentiality test shows, the method may be extended to the case that $ H_0 $ H0 is composite. Date: 2017 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:29:y:2017:i:2:p:167-188 Ordering information: This journal article can be ordered from DOI: 10.1080/10485252.2017.1285029 Access Statistics for this article Journal of Nonparametric Statistics is currently edited by Jun Shao More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.