论文标题
超品质估计的随机近似算法
Stochastic approximation algorithms for superquantiles estimation
论文作者
论文摘要
本文致力于两种不同的两次尺度随机近似算法，用于超品质估计。我们将研究Robbins-Monro估计量及其共染色版本的渐近行为。我们的主要贡献是通过Martingale方法确定几乎确定的融合，二次强法和迭代对数定律。还提供了联合渐近正态性。我们的理论分析通过实际数据集的数值实验说明了。
This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexified 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.
