讲座题目：Self-normalization for Stationarity of Irregular Spatial Data

主 讲 人：张荣茂

讲座时间：2022年5月18日（周三）下午13：30-14：30

地点：综合楼644会议室

主讲人简介：

      张荣茂，浙江大学数学科学学院教授、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和省部级基金项目多项，现任J. Korean Statist. Soc.（SCI期刊）和Intern. J. Math. Statist.的副主编。

讲座摘要：

      Due to the fact that the Discrete Fourier Transform (DTF) at different frequencies are asymptotically uncorrelated for stationary random fields and asymptotically correlated for non-stationary cases, a test for stationarity based on weighted DFT covariance will be discussed in this talk. Since using such a test directly will involve nuisance parameters, which are really complicated and difficult to be accurately estimated, the size and power may be very poor. To tackle this issue, a self-normalization procedure is applied and two test statistics based on extreme value and partial sum of the weighted DFT covariance are considered. The new tests not only avoid estimating the nuisance parameter, but also adapt to the whole frequency space. Under regular conditions, the limit distributions of the new tests are developed. Simulations and two data sets are also used to illustrate the proposed test.