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.

翻译：在这项工作中,我们研究一种新的递归性随机算法,用于联合估计一个未知分布的四分位数和超多位数。这种算法的新颖之处是使用超多位数递归近近似值内四分位数估计的Cesaro平均值。我们为不同步数序列的超多位数估测器的二次风险提供了一些尖锐的非保全界限。我们还证明,在Robbbins Monro算法的定量估计及其平均版本上,我们用隐藏在我们随机算法背后的传播近似点来得出了我们联合程序的中央限值。