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Stochastic approximation algorithms for superquantiles estimation

Bercu, B., Costa, Manon and Gadat, Sébastien (2020) Stochastic approximation algorithms for superquantiles estimation. TSE Working Paper, n. 20-1142, Toulouse

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Abstract

This paper is devoted to two dierent two-time-scale stochastic ap-
proximation algorithms for superquantile estimation. We shall investigate the
asymptotic behavior of a Robbins-Monro estimator and its convexied version.
Our main contribution is to establish the almost sure convergence, the quadratic
strong law and the law of iterated logarithm for our estimates via a martingale
approach. A joint asymptotic normality is also provided. Our theoretical analysis is illustrated by numerical experiments on real datasets.

Item Type: Monograph (Working Paper)
Language: English
Date: September 2020
Place of Publication: Toulouse
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 15 Sep 2020 08:40
Last Modified: 15 Sep 2020 08:40
OAI Identifier: oai:tse-fr.eu:124668
URI: http://publications.ut-capitole.fr/id/eprint/41782

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