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dc.contributor.advisorRoyset, Johannes O.
dc.contributor.authorSabol, John J., III
dc.date16-Jun
dc.date.accessioned2016-08-02T19:34:04Z
dc.date.available2016-08-02T19:34:04Z
dc.date.issued2016-06
dc.identifier.urihttp://hdl.handle.net/10945/49377
dc.descriptionApproved for public release; distribution is unlimiteden_US
dc.description.abstractAnalysts often concern themselves with the tail regions of distributions, sometimes called extreme events, in order to measure or predict risk. One risk metric, the superquantile, possesses several properties that make it particularly well-suited for risk quantification. Observable data, however, often lack information on extreme events due to various resource constraints, resulting in sample superquantile estimates that often undervalue the true level of risk. By leveraging the dual relationship between superquantiles and superexpectations, we apply constrained optimization on second-order epi-splines to arrive at incrementally better approximations of superquantile values. With these improved estimates, we incorporate additional constraints to improve the fidelity of density estimates in tail regions. We limit our investigation to data with heavy tails, where risk quantification is typically the most difficult. Demonstrations are provided in the form of a known distributional benchmark, historical financial data, and a fluid dynamics model used in the development of a high-speed naval vessel. Results show that accurate quantile and superquantile constraint implementation, in conjunction with empirical statistics and distributional knowledge, can improve tail density estimates by up to 15% for small samples of various heavy-tailed distributions.en_US
dc.description.urihttp://archive.org/details/dualpproachtosup1094549377
dc.publisherMonterey, California: Naval Postgraduate Schoolen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleDual approach to superquantile estimation and applications to density fittingen_US
dc.typeThesisen_US
dc.contributor.secondreaderButtrey, Samuel E.
dc.contributor.departmentOperations Researchen_US
dc.subject.authorprobability density estimationen_US
dc.subject.authorepi-splinesen_US
dc.subject.authoroptimizationen_US
dc.subject.authorrisk quantificationen_US
dc.subject.authorsuperquantilesen_US
dc.subject.authornon-parametric statisticsen_US
dc.description.serviceCaptain, United States Marine Corpsen_US
etd.thesisdegree.nameMaster of Science in Operations Researchen_US
etd.thesisdegree.levelMastersen_US
etd.thesisdegree.disciplineOperations Researchen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US


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