spatialTailDep: spatialTailDep

In spatialTailDep: Estimation of spatial tail dependence models

Description

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).

Details

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.

References

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.

Examples

## get a list of all help files of user-visible functions in the package
help(package = spatialTailDep)

spatialTailDep documentation built on May 2, 2019, 4:51 a.m.