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

fitcovmat {SpatialExtremes} | R Documentation

## Estimates the covariance matrix for the Smith's model

### 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 Unpublished manuscript.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)

[Package SpatialExtremes version 2.0-5 Index]