  The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating
covariance hyper-parameters are compared, in the context of Kriging with a
misspecified covariance structure. A two-step approach is used. First, the case
of the estimation of a single variance hyper-parameter is addressed, for which
the fixed correlation function is misspecified. A predictive variance based
quality criterion is introduced and a closed-form expression of this criterion
is derived. It is shown that when the correlation function is misspecified, the
CV does better compared to ML, while ML is optimal when the model is
well-specified. In the second step, the results of the first step are extended
to the case when the hyper-parameters of the correlation function are also
estimated from data.
