R: Leave-one-out for a km object

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`

[Package DiceKriging version 1.5.5 Index]