论文标题
在空间依赖项下稀疏和密集功能数据的统一主成分分析
Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency
论文作者
论文摘要
我们考虑在地统计设置下收集的空间依赖功能数据，其中从空间点过程中对位置进行采样。功能响应是在空间依赖的功能效应和空间独立的功能掘金效应的总和。对每个函数的观察都在离散的时间点上进行，并被测量错误污染。在空间平稳性和各向同性的假设下，我们提出了一个时空协方差函数的张量产品样条估计器。当进一步假定核心区域化协方差结构时，我们提出了一种新的功能主成分分析方法，该方法借用了相邻函数的信息。所提出的方法还生成了空间协方差函数的非参数估计器，可用于功能性kriging。在一个统一的框架下，用于稀疏和密集的功能数据，填充和增加的域渐近范式，我们为所提出的估计量开发了渐近收敛速率。通过模拟研究和两个实际数据应用程序，分别代表稀疏和密集的功能数据，证明了所提出方法的优势。
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. 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.
