论文标题
递归超品质近似的非渐近对照
Non asymptotic controls on a recursive superquantile approximation
论文作者
论文摘要
在这项工作中，我们研究了一种新的递归随机算法，用于对未知分布的分位数和超量化的联合估计。该算法的新颖性是在超品质的递归近似值内使用分位数估计的cesaro平均值。我们在不同的步长序列的超品质估计量的二次风险上提供了一些尖锐的非反应界限。我们还证明了Robbins Monro算法上的新的非质子$ l^p $ -Controls用于分位数估计及其平均版本。最后，我们使用隐藏在随机算法后面的扩散近似观点来得出联合程序的中心限制定理。
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.
