Description Details References Examples
The package spatialTailDep
provides functions implementing the pairwise M-estimator of
parametric spatial tail dependence models for distributions attracted to a max-stable law.
This is a rank-based estimator, constructed as the minimizer of the distance between a vector of
integrals of parametric pairwise tail dependence functions and the vector of their empirical counterparts.
It is especially suited for high-dimensional data since it relies on bivariate margins only and, as a consequence of the rank-based
approach, the univariate marginal distributions need not be estimated.
For a complete description of the pairwise M-estimator, see Einmahl et al. (2014).
Currently, this package allows for estimation of the Brown-Resnick process and the Gaussian extreme
value process (usually known as the Smith model) in two-dimensional space. The main function of this package is
Mestimator
, but several other functions are exported as well: tailInt
returns the integral of a parametric bivariate stable tail dependence function over the unit square, tailIntEmp
returns the integral of the bivariate empirical stable tail dependence function over the unit square, and
AsymVar
returns the asymptotic variance matrix for a list of pairs of locations defined
by the user.
The function Mestimator
combines these functions: first it computes a
pilot estimator based on the Euclidian distance between the integrals of the parametric and the empirical
stable tail dependence functions, then it calculates a weight matrix, defined as the inverse of the asymptotic
variance matrix in the pilot estimator, and finally it returns the estimator obtained by
replacing the Euclidian distance by a quadratic form based on the weight matrix. More details
about this procedure can be found in Einmahl et al (2014).
The package exports two auxiliary functions as well: the function selectPairIndices
returns
a list of pair indices of locactions, based on either a maximum-distance criterion or on the maximal
number of pairs that the user wants to include. Next, the function pairCoordinates
can be
used to select the pairs with these indices from a list of location coordinates.
Einmahl, J.H.J., Kiriliouk, A., Krajina, A. and Segers, J., "An M-estimator of spatial tail dependence". See http://arxiv.org/abs/1403.1975.
1 2 | ## get a list of all help files of user-visible functions in the package
help(package = spatialTailDep)
|
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