leaveOneOutFun.Kriging {rlibkriging}

Compute Leave-One-Out (LOO) error for an object with S3 class "Kriging" representing a kriging model.

Description

The returned value is the sum of squares \sum_{i=1}^n [y_i - \hat{y}_{i,(-i)}]^2 where \hat{y}_{i,(-i)} is the prediction of y_i based on the the observations y_j with j \neq i.

Usage

## S3 method for class 'Kriging'
leaveOneOutFun(object, theta, grad = FALSE, bench = FALSE, ...)

Arguments

object

A Kriging object.

theta

A numeric vector of range parameters at which the LOO will be evaluated.

grad

Logical. Should the gradient (w.r.t. theta) be returned?

bench

Logical. Should the function display benchmarking output

...

Not used.

Value

The leave-One-Out value computed for the given vector \boldsymbol{\theta} of correlation ranges.

Author(s)

Yann Richet [e-mail]

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective = "LOO", optim="BFGS")
print(k)

loo <-  function(theta) leaveOneOutFun(k, theta)$leaveOneOut
t <-  seq(from = 0.001, to = 2, length.out = 101)
plot(t, loo(t), type = "l")
abline(v = k$theta(), col = "blue")