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Joint tail modeling via regular variation with applications in climate and environmental studies

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dc.contributor.authorWeller, Grant B., author
dc.contributor.authorCooley, Dan, advisor
dc.contributor.authorBreidt, F. Jay, committee member
dc.contributor.authorEstep, Donald, committee member
dc.contributor.authorSchumacher, Russ, committee member
dc.date.accessioned2007-01-03T05:36:15Z
dc.date.available2007-01-03T05:36:15Z
dc.date.issued2013
dc.description.abstractThis dissertation presents applied, theoretical, and methodological advances in the statistical analysis of multivariate extreme values, employing the underlying mathematical framework of multivariate regular variation. Existing theory is applied in two studies in climatology; these investigations represent novel applications of the regular variation framework in this field. Motivated by applications in environmental studies, a theoretical development in the analysis of extremes is introduced, along with novel statistical methodology. This work first details a novel study which employs the regular variation modeling framework to study uncertainties in a regional climate model's simulation of extreme precipitation events along the west coast of the United States, with a particular focus on the Pineapple Express (PE), a special type of winter storm. We model the tail dependence in past daily precipitation amounts seen in observational data and output of the regional climate model, and we link atmospheric pressure fields to PE events. The fitted dependence model is utilized as a stochastic simulator of future extreme precipitation events, given output from a future-scenario run of the climate model. The simulator and link to pressure fields are used to quantify the uncertainty in a future simulation of extreme precipitation events from the regional climate model, given boundary conditions from a general circulation model. A related study investigates two case studies of extreme precipitation from six regional climate models in the North American Regional Climate Change Assessment Program (NARCCAP). We find that simulated winter season daily precipitation along the Pacific coast exhibit tail dependence to extreme events in the observational record. When considering summer season daily precipitation over a central region of the United States, however, we find almost no correspondence between extremes simulated by NARCCAP and those seen in observations. Furthermore, we discover less consistency among the NARCCAP models in the tail behavior of summer precipitation over this region than that seen in winter precipitation over the west coast region. The analyses in this work indicate that the NARCCAP models are effective at downscaling winter precipitation extremes in the west coast region, but questions remain about their ability to simulate summer-season precipitation extremes in the central region. A deficiency of existing modeling techniques based on the multivariate regular variation framework is the inability to account for hidden regular variation, a feature of many theoretical examples and real data sets. One particular example of this deficiency is the inability to distinguish asymptotic independence from independence in the usual sense. This work develops a novel probabilistic characterization of random vectors possessing hidden regular variation as the sum of independent components. The characterization is shown to be asymptotically valid via a multivariate tail equivalence result, and an example is demonstrated via simulation. The sum characterization is employed to perform inference for the joint tail of random vectors possessing hidden regular variation. This dissertation develops a likelihood-based estimation procedure, employing a novel version of the Monte Carlo expectation-maximization algorithm which has been modified for tail estimation. The methodology is demonstrated on simulated data and applied to a bivariate series of air pollution data from Leeds, UK. We demonstrate the improvement in tail risk estimates offered by the sum representation over approaches which ignore hidden regular variation in the data.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierWeller_colostate_0053A_11644_opt.pdf
dc.identifier.urihttp://hdl.handle.net/10217/79439
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectair pollution
dc.subjectEM algorithm
dc.subjectextreme precipitation
dc.subjectextreme value theory
dc.subjecthidden regular variation
dc.subjectregional climate models
dc.titleJoint tail modeling via regular variation with applications in climate and environmental studies
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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