STOCHASTIC APPROXIMATION ALGORITHMS FOR SUPERQUANTILES ESTIMATION

Bernard Bercu (1) , Manon Costa (2) , Sébastien Gadat (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IMT - Institut de Mathématiques de Toulouse UMR5219

This paper is devoted to two different two-timescale 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.

Domaines: Mathématiques [math]; Probabilités [math.PR]; Statistiques [math.ST]

Bernard Bercu, Manon Costa, Sébastien Gadat. STOCHASTIC APPROXIMATION ALGORITHMS FOR SUPERQUANTILES ESTIMATION. 2020. ⟨hal-02908351⟩