时 间：2026年10月22日 15:30 -16:30
地 点：普陀校区理科大楼A1514室
报告人：温灿红 中国科学技术大学教授
主持人：唐炎林 华东师范大学统计学院
摘 要：
Our proposed approach addresses the challenges associated with nonparametric two-sample testing for densely measured functional data. These challenges stem from the high dimensionality of data and the nature of the observation scheme. We introduce a novel metric concept for random functions known as Grothendieck’s divergence to overcome these challenges, which satisfies the homogeneity-zero equivalence property. Our approach uses a pre-smoothing technique on densely measured functional data and subsequently applies the empirical statistic to estimated curves. We establish the convergence rate of the test statistic without finite moment conditions and derive its asymptotic distributions under both null and alternative hypotheses. Due to the intractability of the limiting null distribution, we employ a permutation test to determine the critical value. Remarkably, our method achieves minimax optimality in the permutation test. This notable result has profound implications and validates the superiority of our proposed method. Our approach is highly versatile and suitable for handling various measurement error distributions. It also demonstrates robustness to heavy-tailed data or outliers through the -contamination model, rendering it an ideal choice for real-world scenarios. Through extensive numerical studies and real data analysis, we showcase that our method outperforms existing approaches in accuracy and robustness.
报告人简介：
温灿红是中国科学技术大学科技商学院、管理学院统计与金融系特任教授、博士生导师。研究方向主要包括高维统计优化和推断、统计学习，以及影像遗传学中的大规模数据分析等。在PNAS、JASA等期刊和计算机顶会ICML上发表多篇学术论文。