Stochastic approximation algorithms for superquantiles estimation

Bernard Bercu, Sébastien Gadat and Manon Costa
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Bernard Bercu: UB - Université de Bordeaux
Sébastien Gadat: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Manon Costa: IUF - Institut universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche

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Abstract: This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile, also known as conditional value-at-risk, estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexified version. Our main contribution is to establish the almost sure convergence, the quadratic strong law and the law of iterated logarithm for our estimates via a martingale approach. A joint asymptotic normality is also provided. Our theoretical analysis is illustrated by numerical experiments on real datasets.

Keywords: Stochastic approximation; Quantile and superquantile; Conditional value-at-risk; Limit theorems (search for similar items in EconPapers)
Date: 2021-06
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Citations: View citations in EconPapers (1)

Published in Electronic Journal of Probability, 2021, 26, pp.1-29. ⟨10.1214/21-EJP648⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03352812

DOI: 10.1214/21-EJP648

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