  Informative sampling designs can impact spatial prediction, or kriging, in
two important ways. First, the sampling design can bias spatial covariance
parameter estimation, which in turn can bias spatial kriging estimates. Second,
even with unbiased estimates of the spatial covariance parameters, since the
kriging variance is a function of the observation locations, these estimates
will vary based on the sample and overestimate the population-based estimates.
In this work, we develop a weighted composite likelihood approach to improve
spatial covariance parameter estimation under informative sampling designs.
Then, given these parameter estimates, we propose three approaches to quantify
the effects of the sampling design on the variance estimates in spatial
prediction. These results can be used to make informed decisions for
population-based inference. We illustrate our approaches using a comprehensive
simulation study. Then, we apply our methods to perform spatial prediction on
nitrate concentration in wells located throughout central California.
