B0497
Title: Space-time covariance models on networks
Authors: Jun Tang - University of Iowa (United States) [presenting]
Dale Zimmerman - University of Iowa (Austria)
Abstract: The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial domain is either a finite-dimensional Euclidean space or a sphere, counterpart developments on a generalized linear network are practically non-existent. To fill this gap, we develop a broad range of parametric, non-separable space-time covariance models on generalized linear networks. For the important subgroup of Euclidean trees, we develop models by the space embedding technique, in concert with the generalized Gneiting class of models and 1-symmetric characteristic functions, and by the convex cone and scale mixture approaches. We give examples from each class of models and investigate the geometric features of these covariance functions near the origin and at infinity. We also reveal connections between different classes of space-time covariance models on Euclidean trees. We conclude by investigating the performance of maximum likelihood estimators of certain proposed models in a simulation study.