Print Email Facebook Twitter Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spaces Title Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spaces Author Kirchner, K. (TU Delft Analysis; TU Delft Delft Institute of Applied Mathematics) Bolin, David (King Abdullah University of Science and Technology) Department Delft Institute of Applied Mathematics Date 2022 Abstract Optimal linear prediction (aka. kriging) of a random field {Z(x)} x∈X indexed by a compact metric space (X, dX ) can be obtained if the mean value function m: X →R and the covariance function ∂: X × X →R of Z are known. We consider the problem of predicting the value of Z(x*) at some location x*∈ X based on observations at locations {xj }nj =1, which accumulate at x*as n→∞(or, more generally, predicting φ(Z) based on {φj (Z)}nj =1 for linear functionals φ,φ1, . . . , φn). Our main result characterizes the asymptotic performance of linear predictors (as n increases) based on an incorrect second-order structure (m, ∂), without any restrictive assumptions on ,∂ ∂ such as stationarity.We, for the first time, provide necessary and sufficient conditions on (m,∂) for asymptotic optimality of the corresponding linear predictor holding uniformly with respect to φ. These general results are illustrated by weakly stationary random fields on X ⊂ Rd with Matérn or periodic covariance functions, and on the sphere X = S2 for the case of two isotropic covariance functions. Subject approximation in Hilbert spacesKrigingspatial statistics To reference this document use: http://resolver.tudelft.nl/uuid:89cb5114-d9d3-45a3-9166-77956807cd50 DOI https://doi.org/10.1214/21-AOS2138 ISSN 0090-5364 Source Annals of Statistics, 50 (2), 1038-1065 Part of collection Institutional Repository Document type journal article Rights © 2022 K. Kirchner, David Bolin Files PDF 21_AOS2138.pdf 510.39 KB Close viewer /islandora/object/uuid:89cb5114-d9d3-45a3-9166-77956807cd50/datastream/OBJ/view