文章基本信息

标题：Non asymptotic controls on a recursive superquantile approximation
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作者：Manon Costa ; Sébastien Gadat
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：2
页码：4718-4769
DOI：10.1214/21-EJS1908
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：60F05; 62L20; 62P05; diffusion approximation; non-asymptotic controls; quantile and superquantile; stochastic approximation