This paper is devoted to two dierent two-time-scale stochastic ap- proximation algorithms for superquantile estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexied 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.
B. Bercu, Manon Costa et Sébastien Gadat, « Stochastic approximation algorithms for superquantiles estimation », TSE Working Paper, n° 20-1142, septembre 2020.
TSE Working Paper, n° 20-1142, septembre 2020