Superquantile regression: theory, algorithms, and applications
Miranda, Sofia I.
Royset, Johannes O.
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We present a novel regression framework centered on a coherent and averse measure of risk, the superquantile risk (also called conditional value-at-risk), which yields more conservatively fitted curves than classical least squares and quantile regressions. In contracts to other generalized regression techniques that approximate conditional superquantiles by various combinations of conditional quantiles, we directly and inperfect analog to classical regressional obtain superquantile regression functions as optimal solutions of certain error minimization problems. We show the existence and possible uniqueness of regression functions, discuss the stability of regression functions under perturbations and approximation of the underlying data, and propose an extension of the coefficient of determination R-squared and Cook’s distance for assessing the goodness of fit for both quantile and superquantile regression models. We present two classes of computational methods for solving the superquantile regression problem, compare both methods’ complexity, and illustrate the methodology in eight numerical examples in the areas of military applications, concerning mission employment of U.S. Navy helicopter pilots and Portuguese Navy submarines, reliability engineering, uncertainty quantification, and financial risk management.
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Rockafellar, R. Tyrrell; Royset, Johannes O. (2013);Superquantiles (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 ...
Royset, Johannes O.; Rockafellar, R. Tyrrell (2015-11-05);Superquantiles, which refer to conditional value-at-risk (CVaR) in the same way that quantiles refer to value-at-risk (VaR), have many advantages in the modeling of risk in finance and engineering. However, some applications ...
Sabol, John J., III (Monterey, California: Naval Postgraduate School, 2016-06);Analysts 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 ...