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Journal Articles Electronic Journal of Probability Year : 2021

Stochastic approximation algorithms for superquantiles estimation

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.

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hal-03352812 , version 1 (25-03-2022)

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Bernard Bercu, Sébastien Gadat, Manon Costa. Stochastic approximation algorithms for superquantiles estimation. Electronic Journal of Probability, 2021, 26, pp.1-29. ⟨10.1214/21-EJP648⟩. ⟨hal-03352812⟩
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