R: Estimates the spatial dependence parameter of a max-stable...

lsmaxstab {SpatialExtremes} | R Documentation

## Estimates the spatial dependence parameter of a max-stable process by minimizing least squares.

### Description

Estimates the spatial dependence parameter of a max-stable process by minimizing least squares.

### Usage

    lsmaxstab(data, coord, cov.mod = "gauss", marge = "emp", control =
    list(), iso = FALSE, ..., 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` | 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 `fitextcoeff`.
`control` | The control arguments to be passed to the `optim` function.
`iso` | Logical. If `TRUE`, isotropy is supposed. Otherwise (default), anisotropy is allowed. Currently this is only useful for the Smith model.
`...` | Optional arguments.
`weighted` | Logical. Should weighted least squares be used? See Details.

### 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}^+.

### 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 Unpublished manuscript.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)

    lsmaxstab(data, locations, "gauss")

    ##Force an isotropic model and do not use weights
    lsmaxstab(data, locations, "gauss", iso = TRUE, weighted = FALSE)

[Package SpatialExtremes version 2.0-5 Index]