kjtail: 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(
  xdat,
  qlev,
  ptail = NULL,
  mqu = NULL,
  type = 1,
  ties.method = eval(formals(rank)$ties.method),
  ...
)

Value

a list with elements

p quantile level for estimation
eta matrix of estimated coefficient of tail dependence \(\eta\), and standard errors
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

Arguments

xdat: a matrix of observations
qlev: vector of quantile levels
ptail: tail probability smaller than qlev. Default to NULL
mqu: marginal quantile levels for semiparametric estimation; data above this are modelled using a generalized Pareto distribution. If NULL, empirical estimation is used throughout
type: integer indicating the estimator type
ties.method: method for handling of ties in rank transformation
...: additional arguments, for backward compatibility

Examples

Run this code

d <- 2
rho <- 0.9
Sigma <- matrix(rho, d, d) + diag(1 - rho, d)
eta_true <- 1/sum(Sigma)
data <- rmnorm(
   n = 1e4,
   mu = rep(0, d),
  Sigma = Sigma)
q <- seq(0.95, 0.995, by = 0.005)
kj <- kjtail(xdat = data, qlev = q)
plot(kj)
abline(h = (1+rho)/2, col = 2)

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