报告摘要：While many general goodness of fit tests exist to assess validity of distributional assumptions for univariate data, most of these are either based on properties of individual probability distributions or cumulative distribution functions. These methods do not generalize easily to more complicated forms of data, such as multivariate data, where these distribution functions are computationally intractable to use when the dimensionality of the data is not small, and data on manifolds, where cumulative distribution functions are not even well-defined. Since distributional assumptions can often not be verified for such data, many researchers have shifted toward using resampling procedures that may be too computationallyintensive for practical use in many scenarios. In this paper, we address this problem by presenting novel distribution-free methodology based on nearest neighbor graphs and energy statistics for testing the plausibility that data is sampled from a hypothesized distribution against a general alternative for any data objects that lie in a metric space. The primary assumptions required are only that we are able to estimate parameters for and simulate from the null distribution. We illustrate many key properties of the testing procedure through theoretical results and numerous simulation studies on various types of data.

报告人介绍：徐栋，德克萨斯理工大学在读博士生。研究方向包括非参数拟合优度检验，针对单变量统计量和多变量统计量的置换检验及最邻近算法等。

邀请人：唐煜