SpatialExtremes (version 1.2-0)

fitcovmat: Estimates the covariance matrix for the Smith's model

Description

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

Usage

fitcovmat(data, coord, marge = "mle", iso = FALSE, ..., 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.

marge

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

iso

Logical. If TRUE, isotropy is supposed. Otherwise (default), anisotropy is allowed.

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 Smith'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 Unpublished manuscript.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

fitcovariance, fitmaxstab, fitextcoeff

Examples

require(RandomFields)
n.site <- 50
n.obs <- 100

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

sigma <- matrix(c(200, 0, 0, 200),ncol = 2)
sigma.inv <- solve(sigma)
sqrtCinv <- t(chol(sigma.inv))

model <- list(list(model = "gauss", var = 1, aniso = sqrtCinv / 2))

## Simulate a max-stable process - with unit Frechet margins
ms1 <- MaxStableRF(locations, model = model, maxstable = "Bool", grid = FALSE, n = n.obs)
ms1 <- t(ms1)

fitcovmat(ms1, locations, marge = "emp")

##Force an isotropic model
fitcovmat(ms1, locations, marge = "emp", iso = TRUE)