adf: Estimation of the bivariate angular dependence function

Description

Estimation of the bivariate angular dependence function

Usage

adf(
  xdat,
  qlev = 0.95,
  estimator = c("hill", "mle", "bayes"),
  level = 0.95,
  ties.method = "random",
  angles = seq(0, 1, by = 0.02),
  plot = TRUE
)

Value

a plot of the angular dependence function if plot=TRUE, plus an invisible list with components

angle the sequence of angles in (0,1) at which the lambda values are evaluated
coef point estimates of the angular dependence function
lower level% confidence interval for lambda (lower bound)
upper level% confidence interval for lambda (upper bound)

Arguments

xdat: an \(n\) by \(2\) matrix of multivariate observations
qlev: quantile level on uniform scale at which to threshold data. Default to 0.95
estimator: string indicating the estimation method
level: level for confidence intervals, default to 0.95
ties.method: method for handling of ties in rank transformation
angles: vector of angles at which to evaluate the angular dependence function The confidence intervals are based on normal quantiles. The standard errors for the hill are based on the asymptotic covariance and that of the mle derived using the delta-method. Bayesian posterior predictive interval estimates are obtained using ratio-of-uniform sampling with flat priors: the shape parameters are constrained to lie within the triangle, as are frequentist point estimates which are adjusted post-inference.
plot: logical indicating whether to plot the function, defaults to TRUE

References

J.L. Wadsworth and J.A. Tawn (2013). A new representation for multivariate tail probabilities, Bernoulli, 19(5B), 2689-2714.

Examples

Run this code

set.seed(12)
dat <- mev::rmev(n = 1000, d = 2, model = "log", param = 0.1)
adf(xdat = dat, estimator = 'hill')

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