# 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

 ```1 2``` ```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.

Mathieu Ribatet

## References

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 Unpublished manuscript.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) fitcovmat(data, locations) ##Force an isotropic model fitcovmat(data, locations, iso = TRUE) ```