Empirical estimation of extremal correlation matrix \(\chi\)

Estimates empirically the matrix of bivariate extremal correlation coefficients \(\chi\).

Usage

emp_chi(data, p = NULL)

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

Arguments

data

Numeric \(n \times d\) 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

Value

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

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.

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)
#>      [,1] [,2] [,3] [,4]
#> [1,] 1.00 0.65 0.55 0.45
#> [2,] 0.65 1.00 0.60 0.55
#> [3,] 0.55 0.60 1.00 0.60
#> [4,] 0.45 0.55 0.60 1.00