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Journal articles on the topic 'Superquantiles'

Author: Grafiati

Published: 7 December 2024

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1

Rio, Emmanuel. "Upper bounds for superquantiles of martingales." Comptes Rendus. Mathématique 359, no. 7 (September 17, 2021): 813–22. http://dx.doi.org/10.5802/crmath.207.

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2

Laguel, Yassine, Krishna Pillutla, Jérôme Malick, and Zaid Harchaoui. "Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation." Set-Valued and Variational Analysis 29, no. 4 (December 2021): 967–96. http://dx.doi.org/10.1007/s11228-021-00609-w.

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3

Kala, Zdeněk. "Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles." Symmetry 13, no. 2 (February 4, 2021): 263. http://dx.doi.org/10.3390/sym13020263.

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The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.

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4

Dedecker, Jérôme, and Florence Merlevède. "Central limit theorem and almost sure results for the empirical estimator of superquantiles/CVaR in the stationary case." Statistics 56, no. 1 (January 2, 2022): 53–72. http://dx.doi.org/10.1080/02331888.2022.2043325.

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5

Mafusalov, Alexander, and Stan Uryasev. "CVaR (superquantile) norm: Stochastic case." European Journal of Operational Research 249, no. 1 (February 2016): 200–208. http://dx.doi.org/10.1016/j.ejor.2015.09.058.

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6

Rockafellar, R. Tyrrell, and Johannes O. Royset. "Superquantile/CVaR risk measures: second-order theory." Annals of Operations Research 262, no. 1 (February 9, 2016): 3–28. http://dx.doi.org/10.1007/s10479-016-2129-0.

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7

Laguel, Yassine, Jérôme Malick, and Zaid Harchaoui. "Superquantile-Based Learning: A Direct Approach Using Gradient-Based Optimization." Journal of Signal Processing Systems 94, no. 2 (January 11, 2022): 161–77. http://dx.doi.org/10.1007/s11265-021-01716-5.

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8

Rockafellar, R. T., J. O. Royset, and S. I. Miranda. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk." European Journal of Operational Research 234, no. 1 (April 2014): 140–54. http://dx.doi.org/10.1016/j.ejor.2013.10.046.

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9

Golodnikov, Kuzmenko, and Uryasev. "CVaR Regression Based on the Relation between CVaR and Mixed-Quantile Quadrangles." Journal of Risk and Financial Management 12, no. 3 (June 26, 2019): 107. http://dx.doi.org/10.3390/jrfm12030107.

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A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called CVaR (superquantile) regression. The main statement of this paper is: CVaR linear regression can be reduced to minimizing the Rockafellar error function with linear programming. The theoretical basis for the analysis is established with the quadrangle theory of risk functions. We derived relationships between elements of CVaR quadrangle and mixed-quantile quadrangle for discrete distributions with equally probable atoms. The deviation in the CVaR quadrangle is an integral. We present two equivalent variants of discretization of this integral, which resulted in two sets of parameters for the mixed-quantile quadrangle. For the first set of parameters, the minimization of error from the CVaR quadrangle is equivalent to the minimization of the Rockafellar error from the mixed-quantile quadrangle. Alternatively, a two-stage procedure based on the decomposition theorem can be used for CVaR linear regression with both sets of parameters. This procedure is valid because the deviation in the mixed-quantile quadrangle (called mixed CVaR deviation) coincides with the deviation in the CVaR quadrangle for both sets of parameters. We illustrated theoretical results with a case study demonstrating the numerical efficiency of the suggested approach. The case study codes, data, and results are posted on the website. The case study was done with the Portfolio Safeguard (PSG) optimization package, which has precoded risk, deviation, and error functions for the considered quadrangles.

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10

Labopin-Richard, T., F. Gamboa, A. Garivier, and B. Iooss. "Bregman superquantiles. Estimation methods and applications." Dependence Modeling 4, no. 1 (March 11, 2016). http://dx.doi.org/10.1515/demo-2016-0004.

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AbstractIn thiswork,we extend some parameters built on a probability distribution introduced before to the casewhere the proximity between real numbers is measured by using a Bregman divergence. This leads to the definition of the Bregman superquantile (thatwe can connect with severalworks in economy, see for example [18] or [9]). Axioms of a coherent measure of risk discussed previously (see [31] or [3]) are studied in the case of Bregman superquantile. Furthermore,we deal with asymptotic properties of aMonte Carlo estimator of the Bregman superquantile. Several numerical tests confirm the theoretical results and an application illustrates the potential interests of the Bregman superquantile.

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11

Bercu, Bernard, Manon Costa, and Sébastien Gadat. "Stochastic approximation algorithms for superquantiles estimation." Electronic Journal of Probability 26, e (January 1, 2021). http://dx.doi.org/10.1214/21-ejp648.

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12

Bercu, Bernard, Jérémie Bigot, and Gauthier Thurin. "Monge-Kantorovich superquantiles and expected shortfalls with applications to multivariate risk measurements." Electronic Journal of Statistics 18, no. 2 (January 1, 2024). http://dx.doi.org/10.1214/24-ejs2279.

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13

Meloni, Carlo, and Marco Pranzo. "Evaluation of the quantiles and superquantiles of the makespan in interval valued activity networks." Computers & Operations Research, November 2022, 106098. http://dx.doi.org/10.1016/j.cor.2022.106098.

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14

Costa, Manon, and Sébastien Gadat. "Non asymptotic controls on a recursive superquantile approximation." Electronic Journal of Statistics 15, no. 2 (January 1, 2021). http://dx.doi.org/10.1214/21-ejs1908.

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15

Pillutla, Krishna, Yassine Laguel, Jérôme Malick, and Zaid Harchaoui. "Federated learning with superquantile aggregation for heterogeneous data." Machine Learning, May 16, 2023. http://dx.doi.org/10.1007/s10994-023-06332-x.

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16

Német, Nikolett, Arpad Curko, András Vukics, and Peter Domokos. "Superquantization rule for multistability in driven-dissipative quantum systems." New Journal of Physics, August 28, 2024. http://dx.doi.org/10.1088/1367-2630/ad748f.

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Abstract We present a superquantization rule which indicates the possible robust stationary states of a generic driven-dissipative quantum system. Multistability in a driven cavity mode interacting with a qudit is revealed hence within a simple intuitive picture. The accuracy of the superquantization approach is confirmed by numerical simulations of the underlying quantum model. In the case when the qudit is composed of several two-level emitters coupled homogeneously to the cavity, we demonstrate the robustness of the superquantized steady states to single-emitter decay.

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17

Royset, J. O., L. Bonfiglio, G. Vernengo, and S. Brizzolara. "Risk-Adaptive Set-Based Design and Applications to Shaping a Hydrofoil." Journal of Mechanical Design 139, no. 10 (August 30, 2017). http://dx.doi.org/10.1115/1.4037623.

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The paper presents a framework for set-based design under uncertainty and demonstrates its viability through designing a super-cavitating hydrofoil of an ultrahigh speed vessel. The framework achieves designs that safely meet the requirements as quantified precisely by superquantile measures of risk (s-risk) and reduces the complexity of design under uncertainty. S-risk ensures comprehensive and decision-theoretically sound assessment of risk and permits a decoupling of parametric uncertainty and surrogate (model) uncertainty. The framework is compatible with any surrogate building technique, but we illustrate it by developing for the first time risk-adaptive surrogates that are especially tailored to s-risk. The numerical results demonstrate the framework in a complex design case requiring multifidelity simulation.

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18

Iooss, Bertrand, Vanessa Vergès, and Vincent Larget. "BEPU robustness analysis via perturbed law-based sensitivity indices." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, July 28, 2021, 1748006X2110365. http://dx.doi.org/10.1177/1748006x211036569.

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The “best-estimate plus uncertainty” (BEPU) methodology is the term used in the nuclear engineering community when dealing with uncertainty quantification issues in realistic numerical simulation models. One of the most critical hypothesis in these studies is the choice of the probability distributions of uncertain input variables which are propagated through the model. Bringing stringent justifications to the BEPU approach, especially in a safety study, requires quantifying the impact of potential uncertainty on the input variable distribution. To solve this problem, this paper deepens the robustness analysis based on the “Perturbed Law-based sensitivity Indices” (PLI). The PLI quantifies the impact of a perturbation of an input distribution on the quantity of interest (as a quantile of a model output or a safety margin) in the BEPU study. The mathematical formalism of the PLI is applied to two particular quantities of interest: the quantile and the superquantile. For both quantities, the PLI can be easily computed using a unique Monte-Carlo sample containing model inputs and output. Numerical tests are developed in order to define validity criteria of a PLI-based robustness analysis. The practical use of the method is illustrated on thermal-hydraulic computer experiments, simulating a cold leg Intermediate Break Loss Of Coolant Accident (IBLOCA) in a pressurized water nuclear reactor.

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19

He, Xuming, Kean Ming Tan, and Wen-Xin Zhou. "Robust estimation and inference for expected shortfall regression with many regressors." Journal of the Royal Statistical Society Series B: Statistical Methodology, June 15, 2023. http://dx.doi.org/10.1093/jrsssb/qkad063.

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Abstract Expected shortfall (ES), also known as superquantile or conditional value-at-risk, is an important measure in risk analysis and stochastic optimisation and has applications beyond these fields. In finance, it refers to the conditional expected return of an asset given that the return is below some quantile of its distribution. In this paper, we consider a joint regression framework recently proposed to model the quantile and ES of a response variable simultaneously, given a set of covariates. The current state-of-the-art approach to this problem involves minimising a non-differentiable and non-convex joint loss function, which poses numerical challenges and limits its applicability to large-scale data. Motivated by the idea of using Neyman-orthogonal scores to reduce sensitivity to nuisance parameters, we propose a statistically robust and computationally efficient two-step procedure for fitting joint quantile and ES regression models that can handle highly skewed and heavy-tailed data. We establish explicit non-asymptotic bounds on estimation and Gaussian approximation errors that lay the foundation for statistical inference, even with increasing covariate dimensions. Finally, through numerical experiments and two data applications, we demonstrate that our approach well balances robustness, statistical, and numerical efficiencies for expected shortfall regression.

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