报告题目: Star Discrepancy For New Stratified Random Sampling I: Optimal Expected Star Discrepancy

报告时间:2022年2月24日(星期四), 20:00-21:00

报告地点:广东技术师范大学东校区工业中心506室

内容摘要: We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of ourresults. Firstly, among these newly designed partitions, there is one that minimizes the expected star discrepancy, thus we partly answer an open question in [F. Pausinger, S. Steinerberger, J. Complex. 2016]. Secondly, there are an infinite number of such class of partitions, they generate point sets with smaller expected discrepancy than classical jittered sampling for large sampling number, leading to an open question in [M. Kiderlen, F. Pausinger, Monatsh. Math.2021] being solved. Thirdly, we prove a strong partition principle and generalize the expected star discrepancy under these partition models from L2−discrepancy to star discrepancy, hence an open question in [M. Kiderlen, F. Pausinger, J.Complex. 2021] is answered. In the end, optimal expected star discrepancy upper bound under this class of partitions is given, which is better than using jittered sampling.

报告人简介: 冼军，男，博士，教授，博士生导师，国家优秀青年基金获得者，现任中山大学数学学院副院长、中国数学会理事、广东省数学会理事、广东省工业与应用数学学会副理事长。2004年毕业于中山大学获理学博士学位，同年进入浙江大学博士后流动站，2006年博士后出站至今在中山大学数学学院工作。主要研究方向为小波分析与应用调和分析、采样理论及其在信号处理中的应用。在ACHA，IP，JFAA，PAMS，JAT等国内外主流专业期刊发表多篇关于信号的采样与重构的理论及其应用的论文，部分结果获得同行们的关注。曾作为项目负责人主持多项国家级和省部级基金项目，现作为项目负责人主持国家自然科学基金面上项目一项。2010年入选广东省“千百十”人才工程培养计划。

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