题目：Extensible Grid Sampling for Quantile Estimation with Confidence Intervals

报告人：何志坚 教授 （华南理工大学 数学学院）

时间：2023年7月13日 星期四 上午10:00-11:00

地点：致远楼101室

摘要：Hilbert space-filling curve (HSFC) is continuous mapping from [0,1] to [0,1]^d for any d>1. 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 paper 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 O(n^{−1−1/d}). 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.

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