rc_est.class: An S4 class to represent the estimation of the Return Curve
In ReturnCurves: Estimation of Return Curves

rc_est.class

R Documentation

An S4 class to represent the estimation of the Return Curve

Description

An S4 class to represent the estimation of the Return Curve

Usage

rc_est.class(
  data,
  qmarg,
  constrainedshape,
  w,
  p,
  method,
  q,
  qalphas,
  k,
  constrained,
  tol,
  par_init,
  interval,
  rc
)

Slots

data: A matrix containing the data on the original margins.
qmarg: A vector containing the marginal quantile used to fit the Generalised Pareto Distribution (GPD) for each variable. Default is rep(0.95, 2).
constrainedshape: Logical. If TRUE (Default), the estimated shape parameter of the Generalised Pareto Distribution (GPD) is constrained to strictly above -1.
w: Sequence of rays between 0 and 1. Default is seq(0, 1, by = 0.01).
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.
p: \loadmathjax
Curve survival probability. Must be \mjeqnp < 1-qp < 1-q and \mjeqnp < 1-q_\alphap < 1-qalphas.
q: Marginal quantile used for the min-projection variable \mjeqnT^1 at angle \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 quantile used for the Heffernan and Tawn conditional extremes model \insertCiteHeffernanTawn2004ReturnCurves for each variable, if constrained = TRUE. Default set to 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 set to 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. Default set to 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 set to a vector of 0 of length 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.
rc: A matrix containing the estimates of the Return Curve.