Compute the empirical pairwise Kendall correlation matrix

Estimates Kendall's \(\hat{\tau}\) between every pair of grid cells from the Gaussian scores matrix Z from [hm_pit_transform()]. Implements Eq. 20 of Clavijo Mesa et al. (2026, Copernicus paper).

Usage

hm_empirical_kendall(Z, cell_idx = NULL)

Arguments

Z

Numeric matrix (\(T \times N\)) of centred Gaussian scores from [hm_pit_transform()].

cell_idx

Optional integer vector of column indices. Defaults to all columns.

Value

A symmetric \(N \times N\) matrix of Kendall \(\hat{\tau}\) values in \([-1, 1]\).

Details

For large grids (N > 1000) supply a subsample via cell_idx to keep computation feasible.

References

Clavijo Mesa, M.V., Di Maio, F. & Zio, E. (2026). Reliability Engineering & System Safety, 275, 112830.

See also

[hm_pit_transform()], [hm_empirical_correlogram()]

Examples

if (FALSE) { # \dontrun{
fits <- hm_fit_marginals(X)
pit  <- hm_pit_transform(X, fits)
tau  <- hm_empirical_kendall(pit$Z, cell_idx = 1:30)
range(tau)
} # }