R: Non parametric estimators of the extremal coefficient...

fitextcoeff {SpatialExtremes} | R Documentation

## Non parametric estimators of the extremal coefficient function

### Description

Estimates non parametrically the extremal coefficient function.

### Usage

    fitextcoeff(data, coord, ..., estim = "ST", marge = "emp", prob = 0,
    plot = TRUE, loess = TRUE, method = "BFGS", std.err = TRUE, xlab,
    ylab, angles = NULL, identify = FALSE)

### 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.
`...` | Additional options to be passed to the `plot` function.
`estim` | Character string specifying the estimator to be used. Must be one of "ST" (Schlather and Tawn) or "Smith".
`marge` | Character string specifying how margins are transformed to unit Frechet. Must be one of "emp", "mle" or "none" - see Details
`prob` | The probability related to the threshold. Only useful with the `ST` estimator.
`plot` | Logical. If `TRUE` (default), the extremal coefficient function is plotted
`loess` | If `TRUE` (default), a local polynomial curve is plotted - see function `loess`.
`method` | The optimizer used when fitting the GEV distribution to data. See function `gevmle`.
`std.err` | Logical. If `TRUE`, standard errors are computed. Note that standard errors are not available with the "ST" estimator.
`xlab,ylab` | The x-axis and y-axis labels. May be missing.
`angles` | A numeric vector. A partition of the interval (-π, π) to help detecting anisotropy.
`identify` | Logical. If `TRUE`, users can use the `identify` function to identify pairs of stations on the plot.

### Details

During the estimation procedure, data need to be transformed to unit Frechet margins firts. This can be done in two different ways ; by using the empirical CDF or the GEV ML estimates.

If `marge = "emp"`, then the data are transformed using the following relation:

z_i = - 1 / log(F(y_i))

where y_i are the observations available at location i, F is the empirical CDF and z_i are the observations transformed to unit Frechet scale.

If `marge = "mle"`, then the data are transformed using the MLE of the GEV distribution - see function `gev2frech`.

Lastly, if data are already supposed to be unit Frechet, then no transformation is performed if one passed the option `marge = "frech"`.

If `data` are already componentwise maxima, `prob` should be zero. Otherwise, users have to define a threshold z (large enough) where univariate extreme value arguments are relevant. We define `prob` such that Pr[Z <= z] = prob.

### Value

Plots the extremal coefficient function and returns the points used for the plot. If `loess = TRUE`, the output is a list with argument "ext.coeff" and "loess".

### Author(s)

Mathieu Ribatet

### References

Schlather, M. and Tawn, J. A. (2003) A dependence measure for multivariate and spatial extreme values: Properties and inference. Biometrika 90(1):139–156.

Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.

### See Also

`madogram`

### Examples

    n.site <- 30
    locations <- matrix(runif(2*n.site, 0, 10), ncol = 2)
    colnames(locations) <- c("lon", "lat")

    ##Simulate a max-stable process - with unit Frechet margins
    data <- rmaxstab(50, locations, cov.mod = "gauss", cov11 = 10, cov12 =
    40, cov22 = 220)

    ##Plot the extremal coefficient function
    op <- par(mfrow=c(1,2))
    fitextcoeff(data, locations, estim = "Smith")
    fitextcoeff(data, locations, angles = seq(-pi, pi, length = 4), estim = "Smith")
    par(op)

[Package SpatialExtremes version 2.0-5 Index]