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

In SpatialExtremes: Modelling Spatial Extremes

Description

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

Usage

fitcovmat(data, coord, marge = "emp", iso = FALSE, control = list(),
..., start, 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.
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.
control	The control arguments to be passed to the optim function.
...	Optional arguments to be passed to the optim function.
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.
weighted	Logical. Should weighted least squares be used?

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 Smith's model and s_{i,j} are the standard errors related to the estimates θ_{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 Unpublished manuscript.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)

fitcovmat(data, locations)

##Force an isotropic model
fitcovmat(data, locations, iso = TRUE)

Example output

        Estimator: Least Squares 
            Model: Smith 
         Weighted: TRUE 
  Objective Value: 887.0233 
Covariance Family: Gaussian 

Estimates
  Marginal Parameters:
  Not estimated.
  Dependence Parameters:
 cov11   cov12   cov22  
153.22   50.56  258.75  

Optimization Information
  Convergence: successful 
  Function Evaluations: 96 

        Estimator: Least Squares 
            Model: Smith 
         Weighted: TRUE 
  Objective Value: 1229.958 
Covariance Family: Gaussian 

Estimates
  Marginal Parameters:
  Not estimated.
  Dependence Parameters:
  cov  
191.1  

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

SpatialExtremes documentation built on Sept. 1, 2020, 3:01 a.m.