copula (version 0.9-5)

Anfun: Nonparametric rank-based estimators of the Pickands dependence function in the bivariate case

Description

Nonparametric rank-based estimators of the Pickands dependence function studied in Genest and Segers (2009).

Usage

Anfun(x, w, estimator = "CFG", corrected = TRUE)

Arguments

x

a two-column data matrix that will be transformed to pseudo-observations.

w

a vector of points in [0,1] where to evaluate the estimated Pickands dependence function.

estimator

specifies which nonparametric rank-based estimator of the unknown Pickands dependence function to use; can be either "CFG" (Caperaa-Fougeres-Genest) or "Pickands".

corrected

TRUE means that the estimators will be corrected to ensure that their value at 0 and 1 is 1.

Value

• Returns a vector containing the values of the estimated Pickands dependence function at the points in w.

Details

More details can be found in Genest and Segers (2009).

References

C. Genest and J. Segers (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics, 37, pages 2990-3022.

See Also

evTestC, evTestK, evCopula, gofEVCopula.

Examples

## True Pickands dependence functions
curve(Afun(gumbelCopula(4), x), 0, 1)
curve(Afun(gumbelCopula(2), x), add=TRUE)
curve(Afun(gumbelCopula(1.33), x), add=TRUE)

## CFG estimator
curve(Anfun(rcopula(gumbelCopula(4), 1000), x), lty=2, add=TRUE)
curve(Anfun(rcopula(gumbelCopula(2), 1000), x),  lty=2, add=TRUE)
curve(Anfun(rcopula(gumbelCopula(1.33), 1000), x),  lty=2, add=TRUE)

## Pickands estimator
curve(Anfun(rcopula(gumbelCopula(4), 1000), x, estimator="Pickands"),
      lty=3, add=TRUE)
curve(Anfun(rcopula(gumbelCopula(2), 1000), x, estimator="Pickands"),
      lty=3, add=TRUE)
curve(Anfun(rcopula(gumbelCopula(1.33), 1000), x, estimator="Pickands"),
      lty=3, add=TRUE)