R: Estimates the covariance function for the Schlather's model

fitcovariance {SpatialExtremes} | R Documentation

## Estimates the covariance function for the Schlather's model

### Description

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

### Usage

    fitcovariance(data, coord, cov.mod, marge = "emp", 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.
`cov.mod` | A character string corresponding the the covariance model in the Schlather's model. Must be one of "whitmat", "cauchy", "powexp", "bessel" or "caugen" for the Whittle-Matern, the Cauchy, the Powered Exponential, the Bessel and the Generalized Cauchy correlation families.
`marge` | Character string specifying how margins are transformed to unit Frechet. Must be one of "emp", "frech" or "mle" - see function `fitextcoeff`.
`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 Schlather'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 Unpublished manuscript.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

`fitcovmat`, `fitmaxstab`, `fitextcoeff`

### Examples

    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
    data <- rmaxstab(50, locations, cov.mod = "whitmat", nugget = 0, range =
    30, smooth = 1)

    fitcovariance(data, locations, "whitmat")

[Package SpatialExtremes version 2.0-5 Index]