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dc.contributor.authorZhang, Chenhua
dc.date.accessioned2014-03-04T02:49:15Z
dc.date.available2014-03-04T02:49:15Z
dc.date.issued2007-08
dc.identifier.otherzhang_chenhua_200708_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/zhang_chenhua_200708_phd
dc.identifier.urihttp://hdl.handle.net/10724/24342
dc.description.abstractThis dissertation focuses on heavy tail analysis. The most important classes of heavy tail distributions are the class of regularly varying distribution functions and the class of subexponential distributions. The class of smoothly varying functions, i.e. functions with continuous derivatives being regularly varying at in¯nity, is a subclass of regularly varying functions. Under an assumption of smooth variation on the step size distribution we obtain higher order expansions for the tail distribution of the global maximum of random walk with negative drift, and under mild regularity conditions that of randomly stopped sums of subexponential random variables with smoothly varying hazard function. Tail index is the key parameter for distributions with regularly varying tail. We study the asymptotic properties of Hill's estimator, one of the commonly used tail index estimators, for shot noise sequences and ¯rst-order bifurcating autoregressive processes.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectHeavy tail analysis
dc.subjectRegularly varying
dc.subjectSubexponential distribution
dc.subjectTail expansion
dc.subjectRandom walk
dc.subjectWiener-Hopf
dc.subjectHill\'s estimator
dc.subjectShot noise processes
dc.subjectBifurcating autoregressive processes
dc.titleApplications of smoothly varying functions and tail index estimation
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentStatistics
dc.description.majorStatistics
dc.description.advisorWilliam P. McCormick
dc.description.committeeWilliam P. McCormick
dc.description.committeeXiangrong Yin
dc.description.committeeQing Zhang
dc.description.committeeTharuvai N. Sriram
dc.description.committeeLynne Seymour


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