Relevant bibliographies by topics / Superquantiles

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Superquantiles'

Author: Grafiati
Published: 7 December 2024

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Journal articles on the topic "Superquantiles"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Superquantiles"

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Thurin, Gauthier. "Quantiles multivariés et transport optimal régularisé." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0262.

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L’objet d’intérêt principal de cette thèse est la fonction quantile de Monge- Kantorovich. On s’intéresse d’abord à la question cruciale de son estimation, qui revient à résoudre un problème de transport optimal. En particulier, on tente de tirer profit de la connaissance a priori de la loi de référence, une information additionnelle par rapport aux algorithmes usuels, qui nous permet de paramétrer les potentiels de transport par leur série de Fourier. Ce faisant, la régularisation entropique du transport optimal permet deux avantages : la construction d’un algorithme efficace et convergent pour résoudre la version semi-duale de notre problème, et l’obtention d’une fonction quantile empirique lisse et monotone. Ces considérations sont ensuite étendues à l’étude de données sphériques, en remplaçant les séries de Fourier par des harmoniques sphériques, et en généralisant la carte entropique à ce cadre non-euclidien. Le second objectif de cette thèse est de définir de nouvelles notions de superquantiles et d’expected shortfalls multivariés, pour compléter l’information fournie par les quantiles. Ces fonctions caractérisent la loi d’un vecteur aléatoire, ainsi que la convergence en loi, sous certaines hypothèses, et trouvent des applications directes en analyse de risque multivarié, pour étendre les mesures de risque classiques de Value-at-Risk et Conditional-Value-at-Risk
This thesis is concerned with the study of the Monge-Kantorovich quantile function. We first address the crucial question of its estimation, which amounts to solve an optimal transport problem. In particular, we try to take advantage of the knowledge of the reference distribution, that represents additional information compared with the usual algorithms, and which allows us to parameterize the transport potentials by their Fourier series. Doing so, entropic regularization provides two advantages: to build an efficient and convergent algorithm for solving the semi-dual version of our problem, and to obtain a smooth and monotonic empirical quantile function. These considerations are then extended to the study of spherical data, by replacing the Fourier series with spherical harmonics, and by generalizing the entropic map to this non-Euclidean setting. The second main purpose of this thesis is to define new notions of multivariate superquantiles and expected shortfalls, to complement the information provided by the quantiles. These functions characterize the law of a random vector, as well as convergence in distribution under certain assumptions, and have direct applications in multivariate risk analysis, to extend the traditional risk measures of Value-at-Risk and Conditional-Value-at-Risk
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Miranda, Sofia I. "Superquantile regression: theory, algorithms, and applications." Thesis, Monterey, California: Naval Postgraduate School, 2014. http://hdl.handle.net/10945/44618.

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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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Book chapters on the topic "Superquantiles"

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Miranda, Sofia Isabel. "Applying Superquantile Regression to a Real-World Problem: Submariners Effort Index Analysis." In Studies in Big Data, 115–22. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24154-8_14.

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Rockafellar, R. Tyrrell, and Johannes O. Royset. "Superquantiles and Their Applications to Risk, Random Variables, and Regression." In Theory Driven by Influential Applications, 151–67. INFORMS, 2013. http://dx.doi.org/10.1287/educ.2013.0111.

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Conference papers on the topic "Superquantiles"

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Laguel, Yassine, Jerome Malick, and Zaid Harchaoui. "First-Order Optimization for Superquantile-Based Supervised Learning." In 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2020. http://dx.doi.org/10.1109/mlsp49062.2020.9231909.

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Laguel, Yassine, Krishna Pillutla, Jerome Malick, and Zaid Harchaoui. "A Superquantile Approach to Federated Learning with Heterogeneous Devices." In 2021 55th Annual Conference on Information Sciences and Systems (CISS). IEEE, 2021. http://dx.doi.org/10.1109/ciss50987.2021.9400318.

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Reports on the topic "Superquantiles"

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Rockafellar, R. T., and Johannes O. Royset. Superquantile/CVaR Risk Measures: Second-Order Theory. Fort Belvoir, VA: Defense Technical Information Center, July 2014. http://dx.doi.org/10.21236/ada615948.

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Rockafellar, R. T., and Johannes O. Royset. Superquantile/CVaR Risk Measures: Second-Order Theory. Fort Belvoir, VA: Defense Technical Information Center, July 2015. http://dx.doi.org/10.21236/ada627217.

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Journal articles
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