SpatialTools (version 0.5.8)

krige.sk: Performs Simple Kriging

Description

Performs Simple Kriging using y, a vector of length $n$, V, the (positive definite) covariance matrix of the observed responses, Vp, the $np \times np$ covariance matrix of the responses to be predicted, Vop, the $n \times np$ matrix of covariances between the observed responses and the responses to be predicted, and m, a numeric vector of length 1 identifying the value of the mean for each response.

Usage

krige.sk(y, V, Vp, Vop, m = 0, ...)

Arguments

y

The vector of observed responses. Should be a matrix of size $n \times 1$ or a vector of length $n$.

V

The covariance matrix of the observed responses. The size is $n \times n$.

Vp

The covariance matrix of the responses to be predicted. The size is $np \times np$

Vop

The cross-covariance between the observed responses and the responses to be predicted. The size is $n \times np$.

m

A numeric vector of length 1 giving the mean of each response.

...

Several additional arguments may be supplied. If user specifies nsim to be a positive integer, then nsim conditional realizations of the predictive distribution will be generated. If this is less than 1, then no conditional sim

Value

• The function a list containing the following objects:
• pred
  A vector of length $np$ containing the predicted responses.
• mspe
  A vector of length $np$ containing the mean-square prediction error of the predicted responses.
• simulations
  An $n \times nsim$ matrix containing the nsim realizations of the conditional realizations. Each column of the matrix represents a realization of the conditional normal distribution.
• mean
  The mean value (m) originally provided to the function
• .

Details

It is assumed that there are $n$ observed data values and that we wish to make predictions at $np$ locations. The mean is subtracted from each value of y before determining the kriging weights, and then the mean is added onto the predicted response.

References

Statistical Methods for Spatial Data Analysis, Schabenberger and Gotway (2003). See p. 226-228.

Examples

data(toydata)
	y <- as.vector(toydata$y)
	V <- toydata$V
	Vp <- toydata$Vp
	Vop <- toydata$Vop
	krige.sk(y, V, Vp, Vop, m = 2)