Stochastic approximation algorithms for superquantiles estimation
Statistics Theory
2020-07-30 v1 Probability
Statistics Theory
Abstract
This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile 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.
Cite
@article{arxiv.2007.14659,
title = {Stochastic approximation algorithms for superquantiles estimation},
author = {Bernard Bercu and Manon Costa and Sébastien Gadat},
journal= {arXiv preprint arXiv:2007.14659},
year = {2020}
}