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dc.contributor.authorWang, Ruoduen_US
dc.date.accessioned2012-09-20T18:12:13Z
dc.date.available2012-09-20T18:12:13Z
dc.date.issued2012-05-04en_US
dc.identifier.urihttp://hdl.handle.net/1853/44706
dc.description.abstractThis thesis addresses three topics in the area of statistics and probability, with applications in risk management. First, for the testing problems in the high-dimensional (HD) data analysis, we present a novel method to formulate empirical likelihood tests and jackknife empirical likelihood tests by splitting the sample into subgroups. New tests are constructed to test the equality of two HD means, the coefficient in the HD linear models and the HD covariance matrices. Second, we propose jackknife empirical likelihood methods to formulate interval estimations for important quantities in actuarial science and risk management, such as the risk-distortion measures, Spearman's rho and parametric copulas. Lastly, we introduce the theory of completely mixable (CM) distributions. We give properties of the CM distributions, show that a few classes of distributions are CM and use the new technique to find the bounds for the sum of individual risks with given marginal distributions but unspecific dependence structure. The result partially solves a problem that had been a challenge for decades, and directly leads to the bounds on quantities of interest in risk management, such as the variance, the stop-loss premium, the price of the European options and the Value-at-Risk associated with a joint portfolio.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectEmpirical likelihooden_US
dc.subjectHypothesis testingen_US
dc.subjectHigh-dimensional dataen_US
dc.subjectRisk measuresen_US
dc.subjectCopulasen_US
dc.subject.lcshDimensional analysis
dc.subject.lcshAnalysis of covariance
dc.subject.lcshMathematical statistics
dc.subject.lcshData structures (Computer science)
dc.subject.lcshRisk management
dc.titleSome questions in risk management and high-dimensional data analysisen_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: Wang, Shaun; Committee Member: Yuan, Mingen_US


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