光华讲坛——社会名流与企业家论坛第 5748 期

（线上讲座）

主题：Spatially Dependent Functional Data: Covariance Estimation, Principal Component Analysis, and Kriging

主讲人：加州大学河滨分校李业华教授

主持人：统计学院 林华珍教授

时间：2020年7月10日（周五）上午10:00-11:00

直播平台及会议ID：腾讯会议，663 735 110

主办单位：统计研究中心、数据科学与商业智能联合实验室和统计学院 科研处

主讲人简介：

Dr. Yehua Li is Professor in Statistics at University of California at Riverside. He got his Ph.D. in Statistics in 2006 from Texas A&M University. Before joining UCR in 2018, he held faculty positions in the University of Georgia and Iowa State University. He is a Fellow of the American Statistical Association, an Elected Member of the International Statistical Institute, and a recipient of the National Science Foundation CAREER Award in 2012. He is currently serving on the editorial boards of Canadian Journal of Statistics, Journal of Multivariate Analysis and Stat. His research interests include functional and longitudinal data analysis, non- and semi- parametric methods, spatial statistics, measurement error and mixture models.

李业华，现为加州大学河滨分校统计学教授。他于2006年取得德州农工大学(Texas A&M University)统计学博士学位。在2018年加入UCR之前，他曾在乔治亚大学和爱荷华州立大学担任教职。他是ASA的Fellow; ISI的Elected Member。2012年获得美国国家科学基金会(National Science Foundation) CAREER Award。他目前在Canadian Journal of Statistics, Journal of Multivariate Analysis and Stat编委会任职。他的研究兴趣包括函数型数据和纵向数据分析、非参数和半参数方法、空间统计、测量误差和混合模型。

详情请见其个人主页：https://profiles.ucr.edu/app/home/profile/yehuali

内容提要：

We consider spatially dependent functional data collected under a geostatistics setting, where spatial locations are irregular and random. The functional response is the sum of a spatially dependent functional effect and a spatially independent functional nugget effect. Observations on each function are made on discrete time points and contaminated with measurement errors. Under the assumption of spatial stationarity and isotropy, we propose a tensor product spline estimator for the spatio-temporal covariance function. When a coregionalization covariance structure is further assumed, we propose a new functional principal component analysis method that borrows information from neighboring functions. The proposed method also generates nonparametric estimators for the spatial covariance functions, which can be used for functional kriging. Under a unified framework for sparse and dense functional data, infill and increasing domain asymptotic paradigms, we develop the asymptotic convergence rates for the proposed estimators. Advantages of the proposed approach are demonstrated through simulation studies and two real data applications representing sparse and dense functional data, respectively.

我们考虑在地统计学背景下收集的空间相关功能数据，其中空间位置是不规则和随机的。函数型响应变量是空间相关函数效应和空间独立函数块效应的总和。对每个函数的观察都是在离散时间点上进行的，并且受到测量误差的影响。在空间平稳性和各向同性假设下，提出了一种时空协方差函数的张量积样条估计。当进一步假设协方差结构为共区域化时，我们提出了一种新的函数主成分分析方法。该方法还生成了空间协方差函数的非参数估计量，可用于函数kriging。在稀疏和稠密函数数据的统一框架下，我们给出了所提出估计量的渐近收敛速度。通过仿真研究和两个代表稀疏和稠密函数数据的实际数据应用，证明了该方法的优越性。