Krigings over space and time based on latent low-dimensional structures  

作　　者：Da Huang Qiwei Yao Rongmao Zhang 

机构地区：[1]Department of Statistics,Fudan University,Shanghai 200433,China [2]Department of Statistics,London School of Economics,London WC 2A 2AE,UK [3]School of Mathematics,Zhejiang University,Hangzhou 310058,China

出　　处：《Science China Mathematics》2021年第4期823-848,共26页中国科学：数学（英文版）

基　　金：supported by National Statistical Research Project of China(Grant No.2015LY77);National Natural Science Foundation of China(Grant Nos.11571080,11571081,71531006 and 71672042);supported by Engineering and Physical Sciences Research Council(Grant No.EP/L01226X/1);supported by National Natural Science Foundation of China(Grant Nos.11371318 and 11771390);Zhejiang Province Natural Science Foundation(Grant No.R16A010001);the Fundamental Research Funds for the Central Universities。

摘　　要：We propose a new nonparametric approach to represent the linear dependence structure of a spatiotemporal process in terms of latent common factors.Though it is formally similar to the existing reduced rank approximation methods,the fundamental difference is that the low-dimensional structure is completely unknown in our setting,which is learned from the data collected irregularly over space but regularly in time.Furthermore,a graph Laplacian is incorporated in the learning in order to take the advantage of the continuity over space,and a new aggregation method via randomly partitioning space is introduced to improve the efficiency.We do not impose any stationarity conditions over space either,as the learning is facilitated by the stationarity in time.Krigings over space and time are carried out based on the learned low-dimensional structure,which is scalable to the cases when the data are taken over a large number of locations and/or over a long time period.Asymptotic properties of the proposed methods are established.An illustration with both simulated and real data sets is also reported.

关 键 词：aggregation via random partitioning common factors EIGENANALYSIS graph Laplacian nugget effect spatio-temporal processes 

分 类 号：O212.7[理学—概率论与数理统计]