報告題目：Self-normalized Inference for Stationarity of Irregular Spatial Data
報 告 人：張榮茂 教授
所在單位：浙江大學
報告時間：2022年9月14日 星期三 9:00-10:00
報告地點：騰訊會議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.
報告人簡介：張榮茂，浙江大學伟德线上平台教授、數據科學中心兼職教授、浙江大學統計所所長，浙江省現場統計研究所副理事長。2004年在浙江大學獲得博士學位，2004年7月-2006年6月在北京大學從事博士後研究，2006年至今在浙江大學工作，多次訪問香港科大、香港中文大學和倫敦政治經濟學院。主要從事非平穩時間序列和高維空間數據的理論與應用研究，已發表SSCI/SCI論文50多篇，發表的雜志包括Ann. Statist.，J. Amer. Assoc. Statist.，J. Econometrics等。2015年獲浙江省傑出青年基金，主持國家自然科學基金、省重點等省部部級基金項目多項，2021年獲第一屆統計學科學技術進步獎三等獎和浙江省自然科學獎二等獎，現任J. Korean Statist. Soc.（SCI期刊）和Intern. J. Math. Statist.的副主編。Journal of Time Series Analysis, Statistics Sinica等期刊匿名審稿人。
