BERCU, Bernard; COSTA, Manon; GADAT, Sébastien

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BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]

COSTA, Manon
Institut de Mathématiques de Toulouse UMR5219 [IMT]

GADAT, Sébastien
Institut de Mathématiques de Toulouse UMR5219 [IMT]

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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.< Leer menos

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STOCHASTIC APPROXIMATION ALGORITHMS FOR SUPERQUANTILES ESTIMATION

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