Non-asymptotic study of a recursive superquantile estimation algorithm

Manon Costa (1) , Sébastien Gadat (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TSE-R - Toulouse School of Economics

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.

Mots clés: Stochastic approximation; Quantile and superquantile; Non-asymptotic controls; Diffusion approximation

Domaines: Economies et finances

Manon Costa, Sébastien Gadat. Non-asymptotic study of a recursive superquantile estimation algorithm. Electronic Journal of Statistics , 2021, 15 (2), pp.4718-4769. ⟨10.1214/21-EJS1908⟩. ⟨hal-03610477⟩