Non-asymptotic study of a recursive superquantile estimation algorithm

Manon Costa () and Sébastien Gadat
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Manon Costa: IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique
Sébastien Gadat: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Stochastic approximation; Quantile and superquantile; Non-asymptotic controls; Diffusion approximation (search for similar items in EconPapers)
Date: 2021-01
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: View the original document on HAL open archive server: https://hal.science/hal-03610477v1
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Published in Electronic Journal of Statistics , 2021, 15 (2), pp.4718-4769. ⟨10.1214/21-EJS1908⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03610477

DOI: 10.1214/21-EJS1908

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