Non asymptotic controls on a recursive superquantile approximation. (English) Zbl 1471.62443
Summary: 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 \(L^p\)-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.
MSC:
| 62L20 | Stochastic approximation |
| 60F05 | Central limit and other weak theorems |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
stochastic approximation; quantile and superquantile; non-asymptotic controls; diffusion approximationReferences:
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