Rank-based transformation to angular measure

Description

The method uses the pseudo-polar transformation for suitable norms, transforming the data to pseudo-observations, than marginally to unit Frechet or unit Pareto. Empirical or Euclidean weights are computed and return alongside of the angular and radial sample

Usage

angmeas(x, Rnorm = c("l1", "l2", "linf"), Anorm = c("l1", "l2", "linf",
  "arctan"), marg = c("Frechet", "Pareto"), wgt = c("Euclidean",
  "Empirical"))

Arguments

Value

a list with arguments ang for the d-1 pseudo-angular sample, rad with the radial component and wts if Rnorm is set to "l1" (default).

a list with components

• ang matrix of pseudo-angular observations

• rad vector of radial contributions

• wts empirical or Euclidean likelihood weights for observations

Author(s)

Leo Belzile

References

Einmahl, J.H.J. and J. Segers (2009). Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution, Annals of Statistics, 37(5B), 2953–2989.

de Carvalho, M. and B. Oumow and J. Segers and M. Warchol (2013). A Euclidean likelihood estimator for bivariate tail dependence, Comm. Statist. Theory Methods, 42(7), 1176–1192.

Owen, A.B. (2001). Empirical Likelihood, CRC Press, 304p.

Examples

x <- rmev(n=25, d=3, param=0.5, model="log")
wts <- angmeas(x=x, Rnorm="l1", Anorm="l1", marg="Frechet", wgt="Empirical")
wts2 <- angmeas(x=x, Rnorm="l2", Anorm="l2", marg="Pareto", wgt="Euclidean")

Results