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- handle: 10670/1.z2hc27
- hal: hal-03610477
- doi: 10.1214/21-EJS1908
- WOS: 000740666000022
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info:eu-repo/semantics/altIdentifier/doi/10.1214/21-EJS1908
info:eu-repo/semantics/OpenAccess
Mots-clés
Stochastic approximation Quantile and superquantile Non-asymptotic controls Diffusion approximationSujets proches
Gases--Diffusion Liquids--Diffusion broadcastingCiter ce document
Manon Costa et al., « Non-asymptotic study of a recursive superquantile estimation algorithm », HAL-SHS : économie et finance, ID : 10.1214/21-EJS1908
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Résumé
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 thequantile 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.