Non asymptotic controls on a stochastic algorithm for superquantile approximation

Sébastien Gadat () and Manon Costa

No 20-1149, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: In this work, we study a new recursive stochastic algorithm for the joint estimation of quantile and superquantile of an unknown distribution. The novelty of this algorithm is to use the Cesaro averaging of the quantile estimation inside the recursive approximation of the superquantile. We provide some sharp non-asymptotic bounds on the quadratic risk of the superquantile estimator for different step size sequences. We also prove new non-asymptotic Lp-controls on the Robbins Monro algorithm for quantile estimation and its averaged version. Finally, we derive a central limit theorem of our joint procedure using the diffusion approximation point of view hidden behind our stochastic algorithm.

Date: 2020-09-25
New Economics Papers: this item is included in nep-ecm and nep-ore
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