Kernel Approximations for Universal Kriging Predictors

This work derives explicit kernel approximations for universal kriging predictors for a class of intrinsic random function models. This class of predictors is of particular interest because they are equivalent to the standard two-dimensional thin plate smoothing splines. By introducing a continuous version of the intrinsic random function model, we derive a kernel approximation to the universal kriging predictor. The kernel function is the solution to an integral equation subject to some boundary conditions and can be expressed in terms of modified Bessel functions. For moderate sample sizes and a broad range of the signal-to-noise variance ratio, some exact calculations demonstrate that the kernel approximation works very well when the observations lie on a square grid.