Superquantile Regression with Applications to Buffered Reliability, Uncertainty Quantification, and Conditional Value-at-Risk
RocRoyMir.pdf (285.1Kb)Abstract
The paper presents a generalized regression technique centered on a superquantile (also called
conditional value-at-risk) that is consistent with that coherent measure of risk and yields more
conservatively fitted curves than classical least-squares and quantile regression. In contrast to
other generalized regression techniques that approximate conditional superquantiles by various
combinations of conditional quantiles, we directly and in perfect analog to classical regression
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 for assessing the goodness
of fit. The paper presents two numerical methods for solving the error minimization problems
and illustrates the methodology in several numerical examples in the areas of uncertainty quantification, reliability engineering, and financial risk management.
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