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.
Bernard Bercu, Sébastien Gadat, and Manon Costa, “Stochastic approximation algorithms for superquantiles estimation”, Electronic Journal of Probability, vol. 26, n. 84, June 2021, pp. 1–29.
Bernard Bercu, Manon Costa, and Sébastien Gadat, “Stochastic approximation algorithms for superquantiles estimation”, TSE Working Paper, n. 20-1142, September 2020.
TSE Working Paper, n. 20-1142, September 2020