lsmaxstab {SpatialExtremes}

Estimates the spatial dependence parameter of a max-stable process by minimizing least squares.

Description

Estimates the spatial dependence parameter of a max-stable process by minimizing least squares.

Usage

lsmaxstab(data, coord, cov.mod = "gauss", marge = "emp", control =
list(), iso = FALSE, ..., weighted = TRUE)

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

Character string specifying the max-stable process considered. Must be one of "gauss" (Smith's model), "whitmat", "cauchy", "powexp", "bessel", "caugen" for the Schlather model with the corresponding correlation function.

marge

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

control

The control arguments to be passed to the optim function.

iso

Logical. If TRUE, isotropy is supposed. Otherwise (default), anisotropy is allowed. Currently this is only useful for the Smith model.

...

Optional arguments.

weighted

Logical. Should weighted least squares be used? See Details.

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 maxstable model considered and s_{i,j} are the standard errors related to the estimates \tilde{\theta}_{i,j}.

Value

An object of class maxstab.

Author(s)

Mathieu Ribatet

References

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 Unpublished manuscript.

See Also

fitcovariance, fitmaxstab, fitextcoeff

Examples

n.site <- 50
n.obs <- 100
locations <- matrix(runif(2*n.site, 0, 40), ncol = 2)
colnames(locations) <- c("lon", "lat")

## Simulate a max-stable process - with unit Frechet margins
data <- rmaxstab(50, locations, cov.mod = "gauss", cov11 = 200, cov12 =
0, cov22 = 200)

lsmaxstab(data, locations, "gauss")

##Force an isotropic model and do not use weights
lsmaxstab(data, locations, "gauss", iso = TRUE, weighted = FALSE)