Description Usage Arguments Details Value Author(s) See Also Examples

The function estimates the prediction variances by a cross-validation approach (see vignette) applied to each sample means of summary statistics.

1 2 |

`qsd` |
object of class |

`cvm` |
list of prefitted covariance models obtained from function |

`theta` |
optional, default |

`type` |
name of type of prediction variance |

`cl` |
cluster object, |

Other than the kriging prediction variance, which solely depends on interdistances of sample points
and estimated covariance parameters of some assumed to be known spatial covariance model, the cross-validation
based approach (see [4] and the vignette) even takes into account the predicted values at '`theta`

' and thus can be thought of
a more robust measure of variability between different spatial locations. By default, '`theta`

' equals the current sampling set
stored in the object '`qsd`

'.

If we set the type of measure '`type`

' equal to "`cve`

", the impact on the level of accuracy (predicting at unsampled
points) is measured by a *delete-k jackknifed variance* of prediction errors. This approach does not require further
simulation runs as a measure of uncertainty for predicting the sample means of statistics at new candidate points accross the parameter space.
If `attr(cvm,"type")`

equals "`max`

", then the maximum of kriging and CV-based prediction variances is returned.

In addition, other measures of prediction uncertainty are available such as the *root mean square deviation*
(`rmsd`

) and *mean square deviation* (`msd`

) or the *standardized cross-validation error*
(`scve`

). The details are explained in the vignette. In order to assess the predictive quality of possibly
different covariance models (also depending on the initial sample size), including the comparison of different
sizes of initial sampling designs, the following measures [8] are available for covariance model validation and adapted
to the cross-validation approach here by using an *average cross-validation error* (`acve`

), the *mean square error* (`mse`

)
or the *average standardized cross-validation error* (`ascve`

). These last measures can only be computed in case the total number
of sample points equals the number of leave-one-out covariance models. This requires to fit each cross-validation
covariance model by `prefitCV`

using the option '`reduce`

'=`FALSE`

which is then based on exactly
one left-out point. Also, we can calculate the kriging variance at the left-out sample points if we set the option '`type`

'
equal to "`sigK`

".

A matrix of estimated prediction variances for each point given by the argument `theta`

(as rows)
and for each statistic (as columns).

M. Baaske

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
data(normal)
# design matrix and statistics
X <- as.matrix(qsd$qldata[,1:2])
Tstat <- qsd$qldata[grep("^mean[.]",names(qsd$qldata))]
# construct but do not re-estimate
# covariance parameters by REML for CV models
qsd$cv.fit <- FALSE
cvm <- prefitCV(qsd)
theta0 <- c("mu"=2,"sd"=1)
# get mean squared deviation using cross-validation at theta0
crossValTx(qsd, cvm, theta0, type = "msd")
# and kriging variance
varKM(qsd$covT,theta0,X,Tstat)
``` |

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