报告题目：Metric Distribution Function
时 间：2023年9月11日（星期一）09：30
地 点：科研楼18号楼1102
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of the distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in an Euclidean space. Still, without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric only. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces, laying the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop a homogeneity test and a mutual independence test for non-Euclidean random objects and present comprehensive empirical evidence to support the performance of our proposed methods.
报告人简介：王学钦，中国科学技术大学管理学院讲席教授，2003年毕业于纽约州立大学宾汉姆顿分校，教育部高层次人才入选者，曾获得教育部高等学校科学研究优秀成果奖-自然科学奖二等奖。现担任教育部高等学校统计学类专业教学指导委员会委员、中国现场统计研究会副理事长、中国现场统计研究会教育统计与管理分会理事长、统计学国际期刊JASA等的Associate Editor、高等教育出版社Lecture Notes: Data Science, Statistics and Probability系列丛书的副主编。