leaveOneOut.km {DiceKriging} | R Documentation |
Leave-one-out for a km object
Description
Cross validation by leave-one-out for a km
object without noisy observations.
Usage
leaveOneOut.km(model, type, trend.reestim=FALSE)
Arguments
model |
an object of class "km" without noisy observations. |
type |
a character string corresponding to the kriging family, to be chosen between simple kriging ("SK"), or universal kriging ("UK"). |
trend.reestim |
should the trend be reestimated when removing an observation? Default to FALSE. |
Details
Leave-one-out (LOO) consists of computing the prediction at a design point when the corresponding observation is removed from the learning set (and this, for all design points). A quick version of LOO based on Dubrule formula is also implemented; It is limited to 2 cases: type=="SK" & (!trend.reestim)
and type=="UK" & trend.reestim
. Leave-one-out is not implemented yet for noisy observations.
Value
A list composed of
mean |
a vector of length n. The ith coordinate is equal to the kriging mean (including the trend) at the ith observation number when removing it from the learning set, |
sd |
a vector of length n. The ith coordinate is equal to the kriging standard deviation at the ith observation number when removing it from the learning set, |
where n is the total number of observations.
Warning
Kriging parameters are not re-estimated when removing one observation. With few points, the re-estimated values can be far from those obtained with the entire learning set. One option is to reestimate the trend coefficients, by setting trend.reestim=TRUE
.
Author(s)
O. Roustant, D. Ginsbourger, Ecole des Mines de St-Etienne.
References
F. Bachoc (2013), Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification. Computational Statistics and Data Analysis, 66, 55-69. http://www.lpma.math.upmc.fr/pageperso/bachoc/publications.html
N.A.C. Cressie (1993), Statistics for spatial data, Wiley series in probability and mathematical statistics.
O. Dubrule (1983), Cross validation of Kriging in a unique neighborhood. Mathematical Geology, 15, 687-699.
J.D. Martin and T.W. Simpson (2005), Use of kriging models to approximate deterministic computer models, AIAA Journal, 43 no. 4, 853-863.
M. Schonlau (1997), Computer experiments and global optimization, Ph.D. thesis, University of Waterloo.
See Also
predict,km-method
, plot,km-method
,
cv