讲座时间：6月5日（周二）上午 10:00-11:00
讲座地点：统计楼103会议室（闵行校区）
报告题目：New Tests for Equality of Several Covariance Functions for Functional Data
报告人：Jin-Ting Zhang (Department of Statistics and Applied Probability,National University of Singapore)
报告摘要：
In this paper, we propose two new tests for the equality of the covariance functions of several functional populations, namely a quasi GPF test and a quasi Fmax test whose test statistics are obtained via Globalizing aPoint-wise quasi F-test statistic with integration and taking itssupremum over some time interval of interest, respectively. Unlike severalexisting tests, they are scale-invariant in the sense that their teststatistics will not change if we multiply each of the observed functions byany non-zero function of time. We derive the asymptotic random expressionsof the two tests under the null hypothesis and show that under some mildconditions,the asymptotic null distribution of the quasi GPF test is achi-squared-type mixture whose distribution can be well approximated by asimple scaled chi-squared distribution. We also propose a random permutationmethod for approximating the null distributions of the quasiGPF and Fmaxtests. The asymptotic distributions of the two tests under a localalternativeare alsoinvestigated and the two testsare shown to beroot-n consistent. A theoreticalpower comparisonbetweenthe quasi GPFtest and the L2-norm based test proposed in the literature is also given.Simulation studies are presented to demonstrate the finite-sampleperformance ofthe new tests againstfive existing tests. An illustrativeexample is also presented. (This is a joint work with Drs. Jia Guo and BuZhou)
报告人简介：
张金廷教授出生在中国广东省，龙川县。早年在北京大学取得学士学位，在中国科学院应用数学所取得硕士学位，在美国北卡莱那大学教堂山分校取得博士学位，曾在哈佛大学做博士后。先后在美国普林斯顿，罗泽斯特等大学做高级访问学者。现任新加坡国立大学概率统计系终身教授，博士生，博士后导师。他先后培养了数十个硕士和七个博士以及三个博士后。他发表了数十篇学术论文，两本统计专着，和一本学术论文集。他现任和曾任几家学术期刊的编委。他曾是几次大型国际会议的组织委员。张金廷教授现在的研究领域包括非参数统计，纵向数据分析，函数数据分析，高维数据分析等等。