  This work investigates the prediction performance of the kriging predictors.
We derive some error bounds for the prediction error in terms of non-asymptotic
probability under the uniform metric and $L_p$ metrics when the spectral
densities of both the true and the imposed correlation functions decay
algebraically. The Mat\'ern family is a prominent class of correlation
functions of this kind. Our analysis shows that, when the smoothness of the
imposed correlation function exceeds that of the true correlation function, the
prediction error becomes more sensitive to the space-filling property of the
design points. In particular, the kriging predictor can still reach the optimal
rate of convergence, if the experimental design scheme is quasi-uniform. Lower
bounds of the kriging prediction error are also derived under the uniform
metric and $L_p$ metrics. An accurate characterization of this error is
obtained, when an oversmoothed correlation function and a space-filling design
is used.
