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

object without noisy observations.

`leaveOneOut.km(model, type, trend.reestim=FALSE) `

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.

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,

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`

.

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.

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.