报告主题：Two Sample Testing for High-dimensional Functional Data: A Multi-resolution Projection Method

报告内容简介：

Testing the equality of the means in two samples of functional data is a fundamental problem in statistics. Existing research has primarily focused on low-dimensional functional data, which may be invalid when confronted with high-dimensional scenarios. In this study, we propose a novel two-sample test for mean functions of high-dimensional functional data, employing a multi-resolution projection (MRP) technique. We establish the asymptotic normality of the proposed MRP test statistic and investigate its power performance when the dimension of the functional variables is high.  In practice,  functional data are only observed on discrete points. We further explore the influence of function reconstruction on our test statistic theoretically. Finally, we assess the finite-sample performance of our test through extensive simulation studies and demonstrate its applicability via two real data applications. Specifically, the analysis of global climate data reveals notable differences in climate characteristics such as daily maximum air temperature, daily minimum air temperature, and daily precipitation when comparing intermediate greenhouse gas emission pathways (e.g., RCP4.5) to high greenhouse gas emission pathways (e.g., RCP8.5) over mid to long-term periods, with more significant differences in the second 25 years. However, these differences may not be significant when examining the first 25 years.

主讲人简介：

刘吉彩，上海立信会计金融学院副教授。现为中国现场统计学会大数据统计分会理事、统计交叉科学研究分会理事、青年统计学家协会理事。长期从事生存分析、高维数据分析，统计机器学习等方面的科学研究，在国际和国内著名的统计杂志上发表学术论文三十余篇；先后主持国家自然科学基金天元项目、青年项目，教育部人文社会科学研究青年项目。