Extensible grid sampling for quantile estimation with confidence intervals

主讲人：何志坚 华南理工大学教授

时间：2023年7月12日9：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：何志坚，华南理工大学数学学院教授、博导、副院长。2015年于清华大学获得理学博士学位。研究兴趣为随机计算方法与不确定性量化，特别是拟蒙特卡罗方法的理论和应用研究。相关研究成果发表在统计学四大期刊Journal of the Royal Statistical Society: Series B，计算科学重要期刊SIAM Journal on Numerical Analysis，SIAM Journal on Scientific Computing，Mathematics of Computation，和运筹管理权威期刊European Journal of Operational Research等。博士论文获得新世界数学奖银奖。主持两项国家自然科学基金项目以及两项省部级项目。

内容介绍：Hilbert space-filling curve (HSFC) is continuous mapping from to for any . HSFC-based numerical integration of d-dimensional functions uses only one-dimensional (extensible) stratification inputs. It improves the error rate of Monte Carlo sampling while retaining asymptotic normality. This work studies HSFC sampling for quantile estimation. We show that under certain conditions, the HSFC-based quantile estimator is asymptotically normal and the asymptotic variance is of . We then develop an asymptotic confidence interval for quantiles that are estimated via simulation using HSFC. This is joint work with Jingyu Tan and Xiaoqun Wang.