Description Usage Arguments Details Value Author(s) Examples
Approximating the variance-covariance matrix of statistics
1 |
qsd |
object of class |
W |
weight matrix for weighted average approximation |
theta |
parameter vector for weighted average approximation |
cvm |
list of fitted cross-validation models, see |
doInvert |
if |
The function estimates the variance matrix of statistics at some (unsampled) point 'theta
' by either
averaging (the Cholesky decomposed terms or matrix logarithms) over all simulated variance matrices
of statistics at previously evaluated points of the parameter space or by a kriging approach which treats the Cholesky
decomposed terms of each variance matrix as a data vector for kriging.
In addition, a Nadaraya-Watson kernel-weighted average approximation can also be applied in order to bias the variance
estimation towards a more locally weighted estimation, where smaller weights are assigned to points being more
distant to an estimate of the model parameter 'theta
'. A reasonable symmetric weighting matrix
'W
' of size equal to the problem dimension, say q
, can be freely chosen by the user. In addition, the user can select
different types of variance averaging methods such as "cholMean
", "wcholMean
", "logMean
", "wlogMean
",
"kriging
" (kriging variance matrix adding three times the prediction standard errors for each Cholesky entry)
defined by 'qsd$var.type
', where the prefix "w
" indicats its corresponding weighted version of
the approximation type. If 'theta
' is not given, then no prediction variances are included and thus the variance matrix estimate of the statistics only refers to the variances due to simulation replications
and not the ones due to the use of kriging approximations of the statistics. Otherwise, the mean variance matrix estimate is given by
\hat{V}+\textrm{diag}(σ(θ)),
where \hat{V} denotes one of the above variance approximation types.
The prediction variances σ are either derived from the kriging results of statistics or based on a (possibly more robust) cross-validation (CV) approach, see vignette for details.
List of variance matrices with the following structure:
VTX |
variance matrix approximation |
sig2 |
kriging prediction variances of statistics at ' |
var |
matrix ' |
inv |
if applicable, the inverse of either ' |
M. Baaske
1 2 3 |
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