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dc.contributor.authorRockafellar, R. Tyrrell
dc.contributor.authorRoyset, Johannes O.
dc.date.accessioned2014-05-29T23:21:46Z
dc.date.available2014-05-29T23:21:46Z
dc.date.issued2013
dc.identifier.citationTutorials in Operations Research, 2013 Informs
dc.identifier.urihttps://hdl.handle.net/10945/41716
dc.descriptionThe article of record as published may be found at http://dx.doi.org/10.1287 /educ.2013.0lllen_US
dc.description.abstractSuperquantiles (also called conditional values-at-risk) are useful tools in risk modeling and optimization, with expanding roles beyond these areas. This tutorial provides a broad overview of superquantiles and their versatile applications. We see that superquantiles are as fundamental to the description of a random variable as the cumulative distribution function (cdf), they can recover the corresponding quantile function through differentiation, they are dual in some sense to superexpectations, which are convex functions uniquely defining the cdf, and they also characterize convergence in distribution. A superdistribution function defined by superquantiles leads to higher-order superquantiles as well as new measures of risk and error, with important applications in risk modeling and generalized regression.en_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.titleSuperquantiles and Their Applications to Risk, Random Variables, and Regressionen_US
dc.typeArticleen_US
dc.contributor.departmentOperations Research
dc.subject.authorrandom variablesen_US
dc.subject.authorquantilesen_US
dc.subject.authorsuperquantilesen_US
dc.subject.authorsuperexpectationsen_US
dc.subject.authorsuperdistributionsen_US
dc.subject.authorconjugate duality;en_US
dc.subject.authorstochastic dominanceen_US
dc.subject.authormeasures of risken_US
dc.subject.authorvalue-at-risken_US
dc.subject.authorconditional value-at-risken_US
dc.subject.authorgeneralized regressionen_US


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