Estimates the causal tail coefficient between two variables
v1 and v2, given the threshold k.
causal_tail_coeff(v1, v2, k = floor(n^0.4), to_rank = TRUE, both_tails = TRUE)Numeric vectors. Two vectors with n observations.
Positive integer. The number of extreme observations used to
compute the causal tail coefficient. Set by default to
k = floor(n^0.4). It must be greater than 1 and smaller
than n.
Boolean. Are the vectors v1 and v2
already sorted?
Set by default to TRUE.
Boolean. Do you consider both tails when computing the
causal tail coefficient? If both_tails = TRUE, then you use the
\(\Psi\) formulation. If both_tails = FALSE,
then you use the \(\Gamma\) formulation.
Set by default to TRUE.
Numeric --- between 0 and 1.
The causal tail coefficient between v1 and v2.
The causal tail coefficient is defined in the paper "Causal discovery in heavy-tailed models" and has two formulations.
The first formulation is defined in the paper as the
\(\Gamma\)-coefficient, and it considers only the upper tails of the
variables. To use this formulation set both_tails = FALSE.
The second formulation is defined in the paper as the
\(\Psi\)-coefficient, and considers both tails of the variables.
To use this formulation set both_tails = FALSE.
In general, the causal tail coefficient is not symmetric, i.e.,
causal_tail_coeff(v1, v2) != causal_tail_coeff(v2, v1).