kjtail: Estimators of the tail coefficient

In lbelzile/mev: Modelling of Extreme Values

Estimators of the tail coefficient

Description

Estimators proposed by Krupskii and Joe under second order expansion for the coefficient of tail dependence \eta and the joint tail orthant probability

Usage

kjtail(
  data,
  q,
  ptail = NULL,
  mqu,
  type = 1,
  ties.method = eval(formals(rank)$ties.method)
)

Arguments

data	a matrix of observations
q	vector of quantile levels
ptail	tail probability smaller than q. Default to NULL
mqu	marginal quantile levels for semiparametric estimation; data above this are modelled using a generalized Pareto distribution. If missing, empirical estimation is used throughout
type	integer indicating the estimator type
ties.method	method for ties

Value

a list with elements

• p quantile level for estimation

• eta estimated coefficient of tail dependence \eta

• eta_sd estimated standard error of \eta

• k1 parameter of the tail expansion

• pat proportion of observations above the threshold

• lambda tail dependence coefficient (sic)

• tailprob tail probability, if ptail is provided

Note

EXPERIMENTAL. The numerical optimization of the likelihood surface is difficult, as the function is ill-behaved. Visual inspection of estimates is necessary to check for non-convergence.

Examples

d <- 2
rho <- 0.9
Sigma <- matrix(rho, d, d) + diag(1 - rho, d)
eta_true <- 1/sum(Sigma)
data <- mev::mvrnorm(
   n = 1e4,
   mu = rep(0, d),
  Sigma = Sigma)
q <- seq(0.95, 0.995, by = 0.005)
taildep <- kjtail(data = data, q = q)
with(taildep,
 plot(x = 1-pat,
      y = eta,
      ylim = c(0,1),
      panel.first = {abline(h = (1+rho)/2)}))

lbelzile/mev documentation built on June 14, 2025, 6:40 p.m.