报告题目：Self-normalized Inference for Stationarity of Irregular Spatial Data
报 告 人：张荣茂 教授
所在单位：浙江大学
报告时间：2022年9月14日 星期三 9:00-10:00
报告地点：腾讯会议222-450-080
摘要：Stationarity test is an important issue in spatial data analysis. Let Z(s) be a random field and Jn(ω) be its discrete Fourier transform (DFT) at frequency ω. It is known that Jn(ω) at fundamental frequencies are asymptotically uncorrelated if and only if Z(s) is second-order stationary, see Bandyopadhyay and Subba Rao (2017). A test for stationarity based on the sample covariance of Jn(ω) can be constructed. However, such a test always performs very poor because its asymptotic variance is difficult to estimate accurately in finite sample, which leads to small size and power. To address this issue, this paper proposes two self-normalized statistics based on extreme values and partial sum of the sample covariance of the DFTs, which allow the lag order of the frequencies in constructing the statistics to be fixed or divergent. Under certain regular conditions, it is shown that the proposed tests converge to functionals of Brownian motion. Simulations and two real data examples confirm good performance of the proposed extreme test.
报告人简介：张荣茂，浙江大学必威教授、数据科学中心兼职教授、浙江大学统计所所长，浙江省现场统计研究所副理事长。2004年在浙江大学获得博士学位，2004年7月-2006年6月在北京大学从事博士后研究，2006年至今在浙江大学工作，多次访问香港科大、香港中文大学和伦敦政治经济学院。主要从事非平稳时间序列和高维空间数据的理论与应用研究，已发表SSCI/SCI论文50多篇，发表的杂志包括Ann. Statist.，J. Amer. Assoc. Statist.，J. Econometrics等。2015年获浙江省杰出青年基金，主持国家自然科学基金、省重点等省部部级基金项目多项，2021年获第一届统计学科学技术进步奖三等奖和浙江省自然科学奖二等奖，现任J. Korean Statist. Soc.（SCI期刊）和Intern. J. Math. Statist.的副主编。Journal of Time Series Analysis, Statistics Sinica等期刊匿名审稿人。
