Kernel-based threshold selection of Goegebeur, Beirlant and de Wet (2008)

Kernel-based threshold selection of Goegebeur, Beirlant and de Wet (2008)

Usage

thselect.gbw(
  xdat,
  kmax,
  kernel = c("Jackson", "Lewis"),
  rho = c("gbw", "ghp", "fagh", "dk"),
  ...
)

Arguments

xdat

[vector] sample exceedances

kmax

[int] maximum number of exceedances considered

kernel

[string] kernel choice, one of Jackson or Lewis

rho

string for the estimator of the second order regular variation. Can also be a negative scalar

...

additional arguments, for backward compatibility purposes

Value

a list with elements

• k0: number of exceedances

• shape: Hill's shape estimate

• rho: second-order regular variation parameter estimate

• gof: goodness-of-fit statistic for the chosen threshold.

References

Goegebeur , Y., Beirlant , J., and de Wet , T. (2008). Linking Pareto-Tail Kernel Goodness-of-fit Statistics with Tail Index at Optimal Threshold and Second Order Estimation. REVSTAT-Statistical Journal, 6(1), 51–69. <doi:10.57805/revstat.v6i1.57>

Examples

xdat <- rgp(n = 1000, scale = 2, shape = 0.5)
(thselect.gbw(xdat, kmax = 500))
#> Threshold selection method: Jackson kernel 
#> Goegebeur, Beirlant and de Wet (2008)
#> Second-order regular variation index (gbw estimator):  -1.192 
#> Number of exceedances: 140 
#> Selected threshold: 6.42 
#> Shape estimate: 0.724