SpatialExtremes (version 1.2-0)

fitcovariance: Estimates the covariance function for the Schlather's model

Description

Estimates the covariance function for the Schlather's model using non-parametric estimates of the pairwise extremal coefficients.

Usage

fitcovariance(data, coord, cov.mod, marge = "mle", ..., start)

Arguments

data

A matrix representing the data. Each column corresponds to one location.

coord

A matrix that gives the coordinates of each location. Each row corresponds to one location.

cov.mod

A character string corresponding the the covariance model in the Schlather's model. Must be one of "whitmat", "cauchy" or "powexp" for the Whittle-Matern, the Cauchy and the Powered Exponential covariance family. If the prefixes "i" or "g" are

marge

Character string specifying how margins are transformed to unit Frechet. Must be one of "emp", "frech" or "mle" - see function fitextcoeff.

start

A named list giving the initial values for the parameters over which the weighted sum of square is to be minimized. If start is omitted the routine attempts to find good starting values.

...

Optional arguments to be passed to the optim function.

Value

• An object of class maxstab.

Details

The fitting procedure is based on weighted least squares. More precisely, the fitting criteria is to minimize: $$\sum_{i,j} \left(\frac{\tilde{\theta}_{i,j} - \hat{\theta}_{i,j}}{s_{i,j}}\right)^2$$ where $\tilde{\theta}_{i,j}$ is a non parametric estimate of the extremal coefficient related to location i and j, $\hat{\theta}_{i,j}$ is the fitted extremal coefficient derived from the Schlather's model and $s_{i,j}$ are the standard errors related to the estimates $\tilde{\theta}_{i,j}$.

References

Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.

See Also

fitcovmat, fitmaxstab, fitextcoeff

Examples

require(RandomFields)
n.site <- 50
locations <- matrix(runif(2*n.site, 0, 10), ncol = 2)
colnames(locations) <- c("lon", "lat")

##Simulating a max-stable process using RandomFields
##This is the Schlather's approach
ms0 <- MaxStableRF(locations, grid=FALSE, model="wh",
                   param=c(0,1,0,30, 1), maxstable="extr",
                   n = 100)
ms0 <- t(ms0)

fitcovariance(ms0, locations, "whitmat", marge = "emp")