ReturnCurves (version 1.0.1)

rc_est: Estimation of the Return Curve

Description

Estimation of the pp-probability return curve following MurphyBarltropetal2023;textualReturnCurves.

Usage

rc_est(
  margdata,
  w = NULL,
  p,
  method = c("hill", "cl"),
  q = 0.95,
  qalphas = rep(0.95, 2),
  k = 7,
  constrained = FALSE,
  tol = 0.001,
  par_init = rep(0, k - 1)
)

Value

An object of S4 class rc_est.class. This object returns the arguments of the function and extra slot rc

interval:

A vector containing the maximum likelihood estimates from the conditional extremes model, ^1_x y and ^1_y x, if constrained = TRUE. If constrained = FALSE, then c(0, 1) is returned; we note that this has no meaningful interpretation as the estimation is performed in an unconstrained interval.

rc:

A matrix with the estimates of the Return Curve.

Arguments

margdata

An S4 object of class margtransf.class. See margtransf for more details.

w

Sequence of rays between 0 and 1. Default is NULL, where a pre-defined grid is used.

p

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

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.

q

Marginal quantile used to define the threshold u_ of the min-projection variable T^1 at ray (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 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 MurphyBarltropetal2024ReturnCurves. 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 of the Bernstein-Bezier polynomials used for estimation of the angular dependence function with the composite likelihood method MurphyBarltropetal2024ReturnCurves. Default is rep(0, k-1).

Details

Given a probability pp and a joint survival function Pr(X>x, Y>y), the pp-probability return curve is defined as RC(p):=(x, y) R^2: Pr(X>x, Y>y)=p.

This method focuses on estimation of RC(p)RC(p) for small pp near 00, so that (X,Y) are in the tail of the distribution.

Pr(X>x, Y>y) is estimated using the angular dependence function () introduced by WadsworthTawn2013;textualReturnCurves. More details on how to estimate () can be found in adf_est.

The return curve estimation RC(p) is done on standard exponential margins and then back transformed onto the original margins.

References

Examples

library(ReturnCurves)

data(airdata)

n <- dim(airdata)[1]

prob <- 10/n

margdata <- margtransf(airdata)

retcurve <- rc_est(margdata = margdata, p = prob, method = "hill")

plot(retcurve)

# To see the the S4 object's slots
str(retcurve)

# To access the return curve estimation
retcurve@rc

# If constrained = T, the MLE estimates for the conditional extremes model
# can be accessed as
retcurve@interval