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Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions

dc.contributor.authorDunker, Fabian
dc.contributor.authorKlasen, Stephan
dc.contributor.authorKrivobokova, Tatyana
dc.date.accessioned2020-02-06T10:49:00Z
dc.date.available2020-02-06T10:49:00Z
dc.date.issued2019de
dc.relation.ISSN10.1214/19-EJS1628de
dc.identifier.urihttp://resolver.sub.uni-goettingen.de/purl?gs-1/17153
dc.description.abstractRatios of medians or other suitable quantiles of two distributions are widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are available. Inspired by the so-called growth incidence curves introduced in poverty research, we argue that the ratio of quantile functions is a more appropriate and informative tool to compare two distributions. We present an estimator for the ratio of quantile functions and develop corresponding simultaneous confidence bands, which allow to assess significance of certain features of the quantile functions ratio. Derived simultaneous confidence bands rely on the asymptotic distribution of the quantile functions ratio and do not require re-sampling techniques. The performance of the simultaneous confidence bands is demonstrated in simulations. Analysis of expenditure data from Uganda in years 1999, 2002 and 2005 illustrates the relevance of our approach.de
dc.language.isoengde
dc.rightsopenAccess
dc.rights.uri1935-7524
dc.subjectGrowth incidence curve; simultaneous confidence bands; quantile processesde
dc.subject.ddc510
dc.titleAsymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functionsde
dc.typejournalArticlede
dc.identifier.doi10.1214/19-EJS1628
dc.type.versionpublishedVersionde
dc.relation.eISSN1935-7524
dc.bibliographicCitation.volume13de
dc.bibliographicCitation.issue2de
dc.bibliographicCitation.firstPage4391de
dc.bibliographicCitation.lastPage4415de
dc.type.subtypejournalArticle
dc.description.statuspeerReviewedde
dc.bibliographicCitation.journalElectronic Journal of Statisticsde


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