报告题目：An Adaptive Test Based on Kendall's tau for Independence in High Dimensions

报告时间：2024年5月11日下午14：00—15：30

报告地点：北区四号教学楼208报告厅

报告摘要：We consider testing the mutual independency for high-dimensional data. It is known that $L_2$-type statistics have lower power under sparse alternatives and $L_\infty$-type statistics have lower power under dense alternatives in high dimensions. In this talk, we develop an adaptive test based on Kendall's tau to compromise both situations of the alternative, which can automatically be adapted to the underlying data. An adaptive test is very useful in practice as the sparsity or density for a data set is usually unknown. In addition, we establish the asymptotic joint distribution of $L_2$-type and $L_\infty$-type statistics based on Kendall's tau under mild assumptions and the asymptotic null distribution of the proposed statistic. Simulation studies show that our adaptive test performs well in either dense or sparse cases. To illustrate the usefulness and effectiveness of the proposed test, real data sets are also analyzed.

专家介绍：杜江，教授，博士生导师。2016年入选北京工业大学日新人才计划；2019年入选北京市教委青年拔尖人才计划。现为美国数学评论评论员、北京应用统计协会理事、中国青年统计学家协会理事。目前主持国家自然科学基金面上项目1项，中国博士后基金（面上）1项，北京市教委科技计划项目1项，参加国家重点研发计划1项、国家自然科学基金2项、国家社科科学基金2项。已在国内外学术刊物上发表论文30余篇，其中20余篇被SCI检索。研究方向为函数型数据分析、空间数据分析、分位数回归、贝叶斯分析等。