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dc.contributor.authorGong, Yunen_US
dc.date.accessioned2012-06-06T16:42:53Z
dc.date.available2012-06-06T16:42:53Z
dc.date.issued2012-01-17en_US
dc.identifier.urihttp://hdl.handle.net/1853/43581
dc.description.abstractIn 1988, Owen introduced empirical likelihood as a nonparametric method for constructing confidence intervals and regions. Since then, empirical likelihood has been studied extensively in the literature due to its generality and effectiveness. It is well known that empirical likelihood has several attractive advantages comparing to its competitors such as bootstrap: determining the shape of confidence regions automatically using only the data; straightforwardly incorporating side information expressed through constraints; being Bartlett correctable. The main part of this thesis extends the empirical likelihood method to several interesting and important statistical inference situations. This thesis has four components. The first component (Chapter II) proposes a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve in order to overcome the computational difficulty when we have nonlinear constrains in the maximization problem. The second component (Chapter III and IV) proposes smoothed empirical likelihood methods to obtain interval estimation for the conditional Value-at-Risk with the volatility model being an ARCH/GARCH model and a nonparametric regression respectively, which have applications in financial risk management. The third component(Chapter V) derives the empirical likelihood for the intermediate quantiles, which plays an important role in the statistics of extremes. Finally, the fourth component (Chapter VI and VII) presents two additional results: in Chapter VI, we present an interesting result by showing that, when the third moment is infinity, we may prefer the Student's t-statistic to the sample mean standardized by the true standard deviation; in Chapter VII, we present a method for testing a subset of parameters for a given parametric model of stationary processes.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectDiffusion processesen_US
dc.subjectNonparametric likelihooden_US
dc.subjectGARCHen_US
dc.subjectROC curveen_US
dc.subjectValue at Risken_US
dc.subjectEmpirical likelihooden_US
dc.subject.lcshExtremal problems (Mathematics)
dc.subject.lcshGolden section
dc.subject.lcshCalculus of variations
dc.subject.lcshBootstrap (Statistics)
dc.subject.lcshMathematical statistics
dc.titleEmpirical likelihood and extremesen_US
dc.typeDissertationen_US
dc.description.degreePhDen_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Peng, Liang; Committee Member: Houdre, Christian; Committee Member: Huo, Xiaoming; Committee Member: Koltchinskii, Vladimir; Committee Member: Qin, Gengshengen_US


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