SpatialTools (version 0.3.2)

krige.ok: Performs Ordinary Kriging

Description

Performs Ordinary Kriging using y, the $n \times 1$ matrix of observed responses, V, the (positive definite) covariance matrix of the observed responses, Vp, the $np \times np$ covariance matrix of the responses to be predicted, and Vop, the $n \times np$ matrix of covariances between the observed responses and the responses to be predicted.

Usage

krige.ok(y, V, Vp, Vop)

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 $n \times np$

Value

• The function a list containing the following objects:
• pred
  A vector of length $np$ containing the predicted responses.
• mope
  A vector of length $np$ containing the mean-square prediction error of the predicted responses.
• w
  A $np \times n$ matrix containing the kriging weights used to calculate red.
• coeff
  A vector of length $k$ containing the estimated regression coefficients.
• vcov.coeff
  A $k \times k$ matrix containing the (estimated) covariance matrix of the regression coefficients.

Details

It is assumed that there are $n$ observed data values and that we wish to make predictions at $np$ locations. We assume that there are $k$ regression coefficients (including the intercept). Both X and Xp should contain a column of 1's if an intercept is desired.

References

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

Examples

data(toydata)
	y <- toydata$y
	V <- toydata$V
	Vp <- toydata$Vp
	Vop <- toydata$Vop
	krige.ok(y, V, Vp, Vop)