Description Usage Arguments Details Value Author(s) References See Also Examples
Estimates the spatial dependence parameter of a max-stable process by minimizing least squares.
1 2 |
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 |
control |
The control arguments to be passed to the
|
iso |
Logical. If |
... |
Optional arguments. |
weighted |
Logical. Should weighted least squares be used? See Details. |
The fitting procedure is based on weighted least squares. More precisely, the fitting criteria is to minimize:
∑_{i,j} [(θ_{i,j}^+ - θ_{i,j}^*) / s_{i,j}]^2
where θ_{i,j}^+ is a non
parametric estimate of the extremal coefficient related to location
i
and j
, θ_{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 θ_{i,j}^+.
An object of class maxstab.
Mathieu Ribatet
Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.
fitcovariance
, fitmaxstab
,
fitextcoeff
1 2 3 4 5 6 7 8 9 10 11 12 13 | 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)
|
Estimator: Least Squares
Model: Smith
Weighted: TRUE
Objective Value: 837.7369
Covariance Family: Gaussian
Estimates
Marginal Parameters:
Not estimated.
Dependence Parameters:
cov11 cov12 cov22
149.85 -15.58 201.33
Optimization Information
Convergence: successful
Function Evaluations: 96
Estimator: Least Squares
Model: Smith
Weighted: FALSE
Objective Value: 9.396089
Covariance Family: Gaussian
Estimates
Marginal Parameters:
Not estimated.
Dependence Parameters:
cov
168.1
Optimization Information
Convergence: successful
Function Evaluations: 24
Warning message:
In optim(unlist(start), obj.fun, hessian = FALSE, control = control, :
one-dimensional optimization by Nelder-Mead is unreliable:
use "Brent" or optimize() directly
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