fitcovariance {SpatialExtremes} | R Documentation |
Estimates the covariance function for the Schlather's model using non-parametric estimates of the pairwise extremal coefficients.
fitcovariance(data, coord, cov.mod, marge = "mle", ..., start)
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 used then the independent Schlather and geometric Gaussian models are used respectively. |
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. |
The fitting procedure is based on weighted least squares. More precisely, the fitting criteria is to minimize:
sum_{i,j} [(theta_{i,j}^+ - theta_{i,j}^*) / s_{i,j}]^2
where theta_{i,j}^+ is a non
parametric estimate of the extremal coefficient related to location
i
and j
, 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 theta_{i,j}^+.
An object of class maxstab.
Mathieu Ribatet
Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.
fitcovmat
, fitmaxstab
,
fitextcoeff
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")