fitcovmat {SpatialExtremes} | R Documentation |
Estimates the covariance matrix for the Smith's model using non-parametric estimates of the pairwise extremal coefficients.
fitcovmat(data, coord, marge = "mle", iso = FALSE, ..., 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. |
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. |
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 Smith'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 Unpublished manuscript.
fitcovariance
, fitmaxstab
,
fitextcoeff
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)