constrainedKriging: An R-package for customary, constrained and covariance-matching constrained point or block kriging

The article describes the R-package constrainedKriging, a tool for spatial prediction problems that involve change of support. The package provides software for spatial interpolation by constrained (CK), covariance-matching constrained (CMCK), and customary universal (UK) kriging. CK and CMCK yield approximately unbiased predictions of nonlinear functionals of target quantities under change of support and are therefore an attractive alternative to conditional Gaussian simulations. The constrainedKriging package computes CK, CMCK, and UK predictions for points or blocks of arbitrary shape from data observed at points in a two-dimensional survey domain. Predictions are computed for a random process model that involves a nonstationary mean function (modeled by a linear regression) and a weakly stationary, isotropic covariance function (or variogram). CK, CMCK, and UK require the point–block and block–block averages of the covariance function if the prediction targets are blocks. The constrainedKriging package uses numerically efficient approximations to compute these averages. The article contains, apart from a brief summary of CK and CMCK, a detailed description of the algorithm used to compute the point–block and block–block covariances, and it describes the functionality of the software in detail. The practical use of the package is illustrated by a comparison of universal and constrained lognormal block kriging for the Meuse Bank heavy metal data set.