computeCBMeasure {RDM}

Dependence measures for the checkerboard copula

Description

Computes \mu(C^{\#}(A)) for some underlying measure for the checkerboard copula C^{\#}(A). This measure depends only on the input matrix A.

Usage

computeCBMeasure(A, method = c("spearman", "kendall", "bkr", "dss", "zeta1"))

Arguments

A

A (possibly non-square) checkerboard mass density.

method

Determines the underlying dependence measure. Options include "spearman", "kendall", "bkr", "dss", "chatterjee" and "zeta1".

Details

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>.

Value

The value of \mu(C^{\#}(A)). For a sorted A, this corresponds to the rearranged dependence measure R_{\mu}(C^{\#}(A)).

Examples

n <- 10
A <- diag(n)/n
computeCBMeasure(A, method="spearman")