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Non-asymptotic study of a recursive superquantile estimation algorithm

Author

Listed:
  • 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)

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.

Suggested Citation

  • Manon Costa & Sébastien Gadat, 2021. "Non-asymptotic study of a recursive superquantile estimation algorithm," Post-Print hal-03610477, HAL.
    • Handle: RePEc:hal:journl:hal-03610477
    DOI: 10.1214/21-EJS1908
    Note: View the original document on HAL open archive server: https://hal.science/hal-03610477
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    References listed on IDEAS

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    Keywords

    Stochastic approximation; Quantile and superquantile; Non-asymptotic controls; Diffusion approximation;
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