Biography:  Xueqin Wang (Chinese: 王学钦) is a professor of Statistics at the Department of Statistics and Finance, School of Management, University of Science and Technology of China (USTC). He received his bachelor’s degree in mathematics from Nankai University and a Ph.D. degree in statistics from Binghamton University in 1997 and 2003. He has been a member of the Steering Committee for Statistics Education, Ministry of Education since 2013. He serves as an associate editor of the Journal of the American Statistical Association - Applications and Case Studies, an associate editor of the Canadian Journal of Statistics, and an associate editor of Statistics and Its Interface. He also serves as an associate editor of Lecture Notes: Data Science, Statistics and Probability, Higher Education Press. He published over 80 research articles and monographs in theory and applications of statistical methods and several biomedical research areas, including epidemiology, genetics, and mental health. He is interested in Statistical theory and methods in statistical machine learning, biostatistics, social science with particular skills in high-dimensional statistics, non-Euclidean data analysis, Gaussian random field regression analysis, among other areas.， 

Title: Metric distribution function

Abstract: Statistical inference aims to use observed samples to learn the unknown properties of a population. It has become an integral step in scientific reasoning. A building block of nonparametric statistical inference is distribution function. The distribution function and samples are connected to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties in statistics, and this connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces. Those distribution functions are no longer convenient to use or applicable in characterizing the rapidly evolving data objects of complex nature. Thus, 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 a Euclidean space, but without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of novel quasi-distribution functions, or metric distribution functions, for metric space-valued random objects.  We investigate the randomness of the data by the distribution of metric between random object and a fixed location. Working with the distribution of the metric in defining a probability measure is particularly challenging. We overcome this challenge to prove the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces that lie the foundation for conducting rational statistical inference for metric space-valued data. Based on metric distribution function, we develop statistical methods for homogeneity test, mutual independence test, and hierarchical clustering for non-Euclidean random objects, and present comprehensive empirical evidence to support the performance of our proposed methods.