adf_est.class {ReturnCurves}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 (Hill 1975), 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 \(u_\omega\) of the min-projection variable \(T^1\) at ray \(\omega\) \(\left(t^1_\omega = t_\omega - u_\omega | t_\omega > u_\omega\right)\), and/or Hill estimator (Hill 1975). Default is 0.95.

qalphas

A vector containing the marginal quantiles used for the Heffernan and Tawn conditional extremes model (Heffernan and Tawn 2004) 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 (Murphy-Barltrop et al. 2024). 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 \(\beta\) of the Bernstein-Bezier polynomials used for estimation of the angular dependence function with the composite likelihood method (Murphy-Barltrop et al. 2024). Default is rep(0, k-1).

interval

Maximum likelihood estimates \(\hat{\alpha}^1_{x\mid y}\) and \(\hat{\alpha}^1_{y\mid x}\) from the conditional extremes model if constrained = TRUE.

adf

A vector containing the estimates of the angular dependence function.

References

Heffernan JE, Tawn JA (2004). “A conditional approach for multivariate extreme values (with discussion).” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(3), 497-546. doi: 10.1111/j.1467-9868.2004.02050.x, https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9868.2004.02050.x.

Hill BM (1975). “A Simple General Approach to Inference About the Tail of a Distribution.” The Annals of Statistics, 3(5), 1163 – 1174. doi: 10.1214/aos/1176343247.

Murphy-Barltrop CJR, Wadsworth JL, Eastoe EF (2024). “Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function.” 2303.13237.


[Package ReturnCurves version 1.0 Index]