  In practice rarely (if ever) is the spatial covariance known in spatial
prediction problems. Often, prediction is performed after estimated spatial
covariance parameters are plugged into the prediction equation. The estimated
spatial association parameters arealso plugged into the prediction variance of
the spatial predictor. However, simply plugging in spatial covariance parameter
estimates into the prediction variance of the spatial predictor does not take
into account the uncertainty in the true values of the spatial covariance
parameters. Therefore the plug-in prediction variance estimate will
underestimate the true prediction variance of the estimated spatial predictor,
especially for small datasets. We propose a new way to estimate the prediction
variance of the estimated spatial predictor based on a covariance penalty using
parametric bootstrapping. Our new estimator is compared to three other
prediction variance estimators proposed in literature. The new prediction
variance estimator generally performs better than the plug in method for small
datasets with weak spatial association, although sometimes it is second best
among the four prediction variance estimators compared. Furthermore, the new
prediction variance estimator could potentially be used in the case of
non-normal prediction.

Methodology