EstimationGumbel: Estimation of the parameter of the Gumbel model
In tailDepFun: Minimum Distance Estimation of Tail Dependence Models

Description Usage Arguments Details Value References See Also Examples

Estimation the parameter of the Gumbel model, using either the pairwise M-estimator or weighted least squares (WLS).

EstimationGumbel(
  x,
  indices,
  k,
  method,
  biascorr = FALSE,
  k1 = (nrow(x) - 10),
  tau = 5,
  covMat = TRUE
)

`x`	An n x d data matrix.
`indices`	A q x d matrix containing at least 2 non-zero elements per row, representing the values in which we will evaluate the stable tail dependence function. For `method = Mestimator`, this matrix should contain exactly two ones per row.
`k`	An integer between 1 and n - 1; the threshold parameter in the definition of the empirical stable tail dependence function.
`method`	Choose between `Mestimator` and `WLS`.
`biascorr`	For `method = "WLS"` only. If `TRUE`, then the bias-corrected estimator of the stable tail dependence function is used. Defaults to `FALSE`.
`k1`	For `biascorr = TRUE` only. The value of k_1 in the definition of the bias-corrected estimator of the stable tail dependence function.
`tau`	For `biascorr = TRUE` only. The parameter of the power kernel.
`covMat`	A Boolean variable. If `TRUE` (the default), the covariance matrix is calculated. Standard errors are obtained by taking the square root of the diagonal elements.

The matrix indices can be either user defined or returned by selectGrid. For method = "Mestimator", only a grid with exactly two ones per row is accepted, representing the pairs to be used.

For WLS, a list with the following components:

`theta`	The estimator with weight matrix identity.
`covMatrix`	The estimated covariance matrix for the estimator.
`value`	The value of the minimized function at `theta`.

Einmahl, J.H.J., Kiriliouk, A., and Segers, J. (2018). A continuous updating weighted least squares estimator of tail dependence in high dimensions. Extremes 21(2), 205-233.

Einmahl, J.H.J., Kiriliouk, A., Krajina, A., and Segers, J. (2016). An Mestimator of spatial tail dependence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(1), 275-298.

selectGrid

## Generate data with theta = 0.5
set.seed(1)
n <- 1000
cop <- copula::gumbelCopula(param = 2, dim = 3)
data <- copula::rCopula(n = n,copula = cop)
## Transform data to unit Pareto margins
x <- apply(data, 2, function(i) n/(n + 0.5 - rank(i)))
## Define indices in which we evaluate the estimator
indices <- selectGrid(c(0,1), d = 3)
EstimationGumbel(x, indices, k = 50, method = "WLS", biascorr = TRUE)