rc_est.class: 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
)

Arguments

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 Hill1975ReturnCurves, or "cl" to use the smooth estimator based on Bernstein-Bezier polynomials estimated by composite maximum likelihood.

p

Curve survival probability. Must be p < 1-qp < 1-q and p < 1-q_p < 1-qalphas.

q

Marginal quantile used for the min-projection variable T^1 at angle (t^1_ = t_ - u_ | t_ > u_), and/or Hill estimator Hill1975ReturnCurves. Default is 0.95.

qalphas

A vector containing the marginal quantile used for the Heffernan and Tawn conditional extremes model HeffernanTawn2004ReturnCurves 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 MurphyBarltropetal2024ReturnCurves. 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 of the Bernstein-Bezier polynomials used for estimation of the angular dependence function with the composite likelihood method MurphyBarltropetal2024ReturnCurves. Default set to a vector of 0 of length k-1.

interval

Maximum likelihood estimates ^1_x y and ^1_y x from the conditional extremes model if constrained = TRUE.

rc

A matrix containing the estimates of the Return Curve.