Repository logo
 

Linear prediction and partial tail correlation for extremes

Simple item page
dc.contributor.authorLee, Jeongjin, author
dc.contributor.authorCooley, Daniel, advisor
dc.contributor.authorKokoszka, Piotr, committee member
dc.contributor.authorBreidt, Jay, committee member
dc.contributor.authorPezeshki, Ali, committee member
dc.date.accessioned2022-08-29T10:17:01Z
dc.date.available2022-08-29T10:17:01Z
dc.date.issued2022
dc.description.abstractThis dissertation consists of three main studies for extreme value analyses: linear prediction for extremes, uncertainty quantification for predictions, and investigating conditional relationships between variables at their extreme levels. We employ multivariate regular variation to provide a framework for modeling dependence in the upper tail, which is assumed to be a direction of interest. Cooley and Thibaud [2019] consider transformed-linear operations to define a vector space on the nonnegative orthant and show regular variation is preserved by these transformed-linear operations. Extending the approach of Cooley and Thibaud [2019], we first consider the problem of performing prediction when observed values are at extreme levels. This linear approach is motivated by the limitation that traditional extreme value models have difficulties fitting a high dimensional extreme value model. We construct an inner product space of nonnegative random variables from transformed-linear combinations of independent regularly varying random variables. Rather than fully characterizing extremal dependence in high dimensions, we summarize tail behavior via a matrix of pairwise tail dependencies. The projection theorem yields the optimal transformed-linear predictor, which has a similar form to the best linear unbiased predictor in non-extreme prediction. We then quantify uncertainty for the prediction of extremes by using information contained in the tail pairwise dependence matrix. We create the 95% prediction interval based on the geometry of regular variation. We show that the prediction intervals have good coverage in a simulation study as well as in two applications: prediction of high NO2 air pollution levels, and prediction of large financial losses. We also compare prediction intervals with a linear approach to ones with a parametric approach. Lastly, we develop the novel notion of partial tail correlation via projection theorem in the inner product space. Partial tail correlations are the analogue of partial correlations in non-extreme statistics but focus on extremal dependence. Partial tail correlation can be represented by the inner product of prediction errors associated with the previously defined best transformed-linear prediction for extremes. We find a connection between the partial tail correlation and the inverse matrix of tail pairwise dependencies. We then develop a hypothesis test for zero elements in the inverse extremal matrix. We apply the idea of partial tail correlation to assess flood risk in application to extreme river discharges in the upper Danube River basin. We compare the extremal graph constructed from the idea of the partial tail correlation to physical flow connections on the Danube.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierLee_colostate_0053A_17236.pdf
dc.identifier.urihttps://hdl.handle.net/10217/235673
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
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.titleLinear prediction and partial tail correlation for extremes
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.)

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Lee_colostate_0053A_17236.pdf
Size:
1.13 MB
Format:
Adobe Portable Document Format
Description:
Download

Collections

2020-
Theses and Dissertations