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Title: Covariance estimation and principal component analysis for spatially dependent functional data Authors:  Yehua Li - University of California at Riverside (United States) [presenting]
Abstract: Spatially dependent functional data are considered which are collected under a geostatistics setting, where locations are sampled from a spatial point process and a random function is observed at each location. Observations on each function are made on discrete time points and contaminated with measurement errors. The error process at each location is modeled as a non-stationary temporal process rather than white noise. Under the assumption of spatial isotropy, we propose a tensor product spline estimator for the spatio-temporal covariance function. If a coregionalization covariance structure is further assumed, we propose a new functional principal component analysis method that borrows information from neighboring functions. Under a unified framework for both sparse and dense functional data, where the number of observations per curve is allowed to be of any rate relative to the number of functions, we develop the asymptotic convergence rates for the proposed estimators. The proposed methods are illustrated by simulation studies and a motivating example of the home price-rent ratio data in the San Francisco metropolitan area.