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dc.contributor.authorEl Barmi, Hammou
dc.contributor.authorMukerjee, Hari
dc.date.accessioned2012-06-15T18:52:28Z
dc.date.available2012-06-15T18:52:28Z
dc.date.issued2012-05-10
dc.identifier.citationElbarmi H., and Mukerjee H. 2012. "Peakedness and peakedness ordering". Journal of Multivariate Analysis, Available online 10 May 2012en_US
dc.identifier.issn0047-259X
dc.identifier.urihttp://hdl.handle.net/10057/5126
dc.identifier.urihttp://dx.doi.org/10.1016/j.jmva.2012.04.006
dc.descriptionClick on the DOI link below to access the article (may not be free).en_US
dc.description.abstractThe peakedness of a random variable (RV) X about a point a is defined by . A RV X is said to be less peaked about a than a RV Y about b, denoted by X≤pkd(a,b)Y, if P(|X−a|≤x)≤P(|Y−b|≤x) for all x≥0, i.e., |X−a| is stochastically larger than |Y−b|. These generalize the original definitions of Birnbaum (1948) [2] who considered the cases where X and Y were symmetric about a and b, respectively. Statistical inferences about the distribution functions of continuous X and Y under peakedness ordering in the symmetric case have been treated in the literature. Rojo et al. (2007) [13] provided estimators of the distributions in the general case and analyzed their properties. We show that these estimators could have poor asymptotic properties relative to those of the empiricals. We provide improved estimators of the DFs, show that they are consistent, derive the weak convergence of the estimators, compare them with the empirical estimators, and provide formulas for statistical inferences. An example is also used to illustrate our theoretical results.en_US
dc.language.isoen_USen_US
dc.publisherElsevieren_US
dc.relation.ispartofseriesJournal of Multivariate Analysis;Available online 10 May 2012
dc.subjectPeakednessen_US
dc.subjectStochastic orderingen_US
dc.subjectEstimationen_US
dc.subjectHypothesis testingen_US
dc.subjectWeak convergenceen_US
dc.titlePeakedness and peakedness orderingen_US
dc.typeArticleen_US
dc.description.versionPeer reviewed
dc.rights.holderCopyright © 2012, Elsevier


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