emp_chi: Empirical estimation of extremal correlation matrix \eChi

In graphicalExtremes: Statistical Methodology for Graphical Extreme Value Models

Empirical estimation of extremal correlation matrix \eChi

Description

Estimates empirically the matrix of bivariate extremal correlation coefficients \eChi.

Usage

emp_chi(data, p = NULL)

emp_chi_pairwise(data, p = NULL, verbose = FALSE)

Arguments

data	Numeric \nxd matrix, where n is the number of observations and d is the dimension.
p	Numeric scalar between 0 and 1 or NULL. If NULL (default), it is assumed that the data are already on multivariate Pareto scale. Else, p is used as the probability in data2mpareto() to standardize the data.
verbose	Print verbose progress information

Details

emp_chi_pairwise calls emp_chi for each pair of observations. This is more robust if the data contains many NAs, but can take rather long.

Value

Numeric matrix \dxd. The matrix contains the bivariate extremal coefficients \chi_{ij}, for i, j = 1, ..., d.

See Also

Other parameter estimation methods: data2mpareto(), emp_chi_multdim(), emp_vario(), emtp2(), fmpareto_HR_MLE(), fmpareto_graph_HR(), loglik_HR()

Examples

n <- 100
d <- 4
p <- .8
Gamma <- cbind(
  c(0, 1.5, 1.5, 2),
  c(1.5, 0, 2, 1.5),
  c(1.5, 2, 0, 1.5),
  c(2, 1.5, 1.5, 0)
)

set.seed(123)
my_data <- rmstable(n, "HR", d = d, par = Gamma)
emp_chi(my_data, p)

graphicalExtremes documentation built on Nov. 14, 2023, 1:07 a.m.