报告题目：Goodness-of-fit Tests for Heavy-tailed Random Fields

报告时间：2026年4月30日

报告摘要：We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed spatial data, whose asymptotic distribution is a Gaussian random field under a hypothesized max-stable random field. Since the covariance structure of the limiting Gaussian random field lacks an explicit expression, we propose a stationary bootstrap procedure for spatial fields to approximate critical values. Simulation studies confirm the theoretical distributional results, and applications to PM2.5 and temperature data illustrate the practical utility of the proposed method for model assessment.

报告人简介：赵宇微，西交利物浦大学高级讲师。先后在德国乌尔姆大学、比利时天主教鲁汶（法语）大学从事博士后研究工作。2017年至2023年在复旦大学上海数学中心担任青年研究员，2023年后至今在西交利物浦大学数学物理学院担任高级讲师。主要研究方向是极值理论、时间序列分析、傅立叶分析、函数型数据分析等，在《Stochastic processes and their applications》、《Bernoulli》、《Medical Physics》等期刊上发表论文7篇。