报告时间：2022年11月8日（星期二）17:00

报告平台：腾讯会议 ID：514 233 597

报 告 人：杜江 副教授

工作单位：北京工业大学

举办单位：数学学院

报告简介：

Testing high-dimensional data independence is an essential task of multivariate data in many fields. Typically, the quadratic and extreme value type statistics based on the Pearson correlation coefficient are designed to test dense and sparse alternatives for evaluating high-dimensional independence. However, the two existing popular test methods are sensitive to outliers and are invalidated for heavy-tail error distributions. To overcome this problem, we propose a Spearman's footrule rank-based quadratic scheme and an extreme value type statistical test for dense and sparse alternatives, respectively. Under mild conditions, the large sample properties of the resulting test methods are established. Additionally, determining or distinguishing whether the data set has sparse or dense alternatives in practice is challenging. Therefore, we show that the proposed two test statistics are asymptotically independent. By combining the proposed quadratic with extreme value statistics, we develop the max-sum test statistic and establish the asymptotic distribution of the resulting statistical test. The simulation results demonstrate that the proposed max-sum test affords empirical power and robustness, regardless of whether the data is sparse dependence or not.  Finally, we use the Leaf and Parkinson's disease datasets to illustrate the use of the proposed test methods.

报告人简介：

杜江，现为北京工业大学副教授，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项等。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、贝叶斯统计等。