adf_est.class: An S4 class to represent the estimation of the Angular...
In ReturnCurves: Estimation of Return Curves

adf_est.class

R Documentation

An S4 class to represent the estimation of the Angular Dependence Function

Description

An S4 class to represent the estimation of the Angular Dependence Function

Usage

adf_est.class(
  dataexp,
  w,
  method,
  q,
  qalphas,
  k,
  constrained,
  tol,
  par_init,
  interval,
  adf
)

Slots

dataexp: A matrix containing the data on standard exponential margins.
w: Sequence of rays between 0 and 1. Default is NULL, where a pre-defined grid is used.
method: String that indicates which method is used for the estimation of the angular dependence function. Must either be "hill", to use the Hill estimator \insertCiteHill1975ReturnCurves, or "cl" to use the smooth estimator based on Bernstein-Bezier polynomials estimated by composite maximum likelihood.
q: \loadmathjax
Marginal quantile used to define the threshold \mjeqnu_\omega of the min-projection variable \mjeqnT^1 at ray \mjeqn\omega \mjeqn\left(t^1_\omega = t_\omega - u_\omega | t_\omega > u_\omega\right), and/or Hill estimator \insertCiteHill1975ReturnCurves. Default is 0.95.
qalphas: A vector containing the marginal quantiles used for the Heffernan and Tawn conditional extremes model \insertCiteHeffernanTawn2004ReturnCurves for each variable, if constrained = TRUE. Default is rep(0.95, 2).
k: Polynomial degree for the Bernstein-Bezier polynomials used for the estimation of the angular dependence function with the composite likelihood method \insertCiteMurphyBarltropetal2024ReturnCurves. Default is 7.
constrained: Logical. If FALSE (Default) no knowledge of the conditional extremes parameters is incorporated in the angular dependence function estimation.
tol: Convergence tolerance for the composite maximum likelihood procedure. Success is declared when the difference of log-likelihood values between iterations does not exceed this value. Default is 0.0001.
par_init: Initial values for the parameters \mjeqn\beta of the Bernstein-Bezier polynomials used for estimation of the angular dependence function with the composite likelihood method \insertCiteMurphyBarltropetal2024ReturnCurves. Default is rep(0, k-1).
interval: Maximum likelihood estimates \mjeqn\hat\alpha^1_x\mid y and \mjeqn\hat\alpha^1_y\mid x from the conditional extremes model if constrained = TRUE.
adf: A vector containing the estimates of the angular dependence function.