Stochastic approximation algorithms for superquantiles estimation

2020/07/29 by Bernard Bercu, Manon Costa, Bercu, Bernard +3
Mathematics · #62P05 #FOS: Mathematics #Primary : 62L20 #Probability (math.PR) #Secondary : 60F05 #Statistics Theory (math.ST) #math.PR #math.ST #msc:60F05 #msc:62L20 #msc:62P05 #stat.TH

paper · pdf · doi:10.48550/arxiv.2007.14659

arxiv created 2020/07/29 · arxiv updated 2020/07/30

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.

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