Lower truncated Hill threshold selection

Given a sample of positive data with Pareto tail, the algorithm computes the optimal number of order statistics that minimizes the variance of the average left truncated tail index estimator, and uses the relationship to the Hill estimator for the Hall class of distributions to derive the optimal number (minimizing the asymptotic mean squared error) of the Hill estimator. The default value for the second order regular variation index is taken to be \(\rho=-1\).

Usage

thselect.bab(
  xdat,
  kmin = floor(0.2 * length(xdat)),
  kmax = length(xdat) - 1L,
  rho = -1,
  test = FALSE,
  nsim = 999L,
  level = 0.95
)

Arguments

xdat: [vector] positive vector of exceedances
kmin: [int] minimum number of exceedances
kmax: [int] maximum number of exceedances for the estimation of the shape parameter.
rho: [double] scalar for the second order regular variation index, a negative number.
test: [logical] if TRUE, computes the goodness-of-fit statistic for the model using Monte Carlo
nsim: [int] number of replications for Monte Carlo test, used only if test=TRUE.
level: [double] confidence level for test

Value

a list with the number of order statistics for the Hill estimator, k0 and the corresponding shape estimate shape, the average lower-trimmed Hill estimator shape._lth and the number of order statistics upon which the latter is based, k0_lth.

References

Bladt, M., Albrecher, H. & Beirlant, J. (2020) Threshold selection and trimming in extremes. Extremes, 23, 629-665 . doi:10.1007/s10687-020-00385-0