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.
Funding Statement
The authors gratefully acknowledge financial support from the Agence Nationale de la Recherche (MaSDOL grant ANR-19-CE23-0017).
Acknowledgments
The authors warmly thank the two anonymous referees for their insightful comments and constructive suggestions which helped to improve the paper substantially.
Citation
Bernard Bercu. Manon Costa. Sébastien Gadat. "Stochastic approximation algorithms for superquantiles estimation." Electron. J. Probab. 26 1 - 29, 2021. https://doi.org/10.1214/21-EJP648
Information
