Computes \(\mu(C^{\#}(A))\) for some underlying measure for the checkerboard copula \(C^{\#}(A)\). This measure depends only on the input matrix A.
computeCBMeasure(A, method = c("spearman", "kendall", "bkr", "dss", "zeta1"))The value of \(\mu(C^{\#}(A))\). For a sorted A, this corresponds to the rearranged dependence measure \(R_{\mu}(C^{\#}(A))\).
A (possibly non-square) checkerboard mass density.
Determines the underlying dependence measure. Options include "spearman", "kendall", "bkr", "dss", "chatterjee" and "zeta1".
This function computes \(\mu(C^{\#}(A))\) for one of several underlying measures for a given checkerboard copula \(C^{\#}(A)\). Most importantly, the value only depends on the (possibly non-square) matrix \(A\) and implicitly assumes the form of \(C^{\#}(A)\) given in Strothmann, Dette and Siburg (2022) <arXiv:2201.03329>. Currently, the following underlying measures are implemented:
"spearman" Implements the concordance measure Spearman's \(\rho\),
"kendall" Implements the concordance measure Kendall's \(\tau\),
"bkr" Implements the Blum–Kiefer–Rosenblatt \(R\), also known as the \(L^2\)-Schweizer-Wolff-measure <doi:10.1214/aos/1176345528>,
"dss" Implements the Dette-Siburg-Stoimenov measure of complete dependence <doi:10.1111/j.1467-9469.2011.00767.x>, also known as Chatterjee's \(\xi\) <doi:10.1080/01621459.2020.1758115>,
"zeta1" Implements the \(\zeta_1\)-measure of complete dependence established by W. Trutschnig <doi:10.1016/j.jmaa.2011.06.013>.
n <- 10
A <- diag(n)/n
computeCBMeasure(A, method="spearman")
Run the code above in your browser using DataLab