article · Toulouse Capitole Publications (University Toulouse 1 Capitole) · 2021
Non-asymptotic study of a recursive superquantile estimation algorithm
Gadat, Sébastien, Costa, Manon
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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 \nquantile 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.
Cite this paper
Gadat, S., & Costa, M. (2021). Non-asymptotic study of a recursive superquantile estimation algorithm. Toulouse Capitole Publications (University Toulouse 1 Capitole).
Gadat, Sébastien, and Manon Costa. “Non-asymptotic study of a recursive superquantile estimation algorithm.” Toulouse Capitole Publications (University Toulouse 1 Capitole), 2021.
Gadat, Sébastien, and Manon Costa. 2021. “Non-asymptotic study of a recursive superquantile estimation algorithm.” Toulouse Capitole Publications (University Toulouse 1 Capitole).
Gadat, S. and Costa, M. (2021) ‘Non-asymptotic study of a recursive superquantile estimation algorithm’, Toulouse Capitole Publications (University Toulouse 1 Capitole).
@article{gadat2021asymptotic,
title = {{Non-asymptotic study of a recursive superquantile estimation algorithm}},
author = {Gadat, Sébastien and Costa, Manon},
journal = {Toulouse Capitole Publications (University Toulouse 1 Capitole)},
year = {2021}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.