# leaveOneOut.km

##### Leave-one-out for a km object

Cross validation by leave-one-out for a `km`

object without noisy observations.

- Keywords
- models

##### 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

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,

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,

##### 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`

.

##### 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

*Documentation reproduced from package DiceKriging, version 1.5.6, License: GPL-2 | GPL-3*