| Title: | Calculate the AUK Estimator |
| Version: | 0.1.0 |
| Description: | Computes the Area Under the Kendall (AUK) estimator for multivariate independence. The AUK estimator is based on the survival copula and quantifies the deviation from the null hypothesis of independence. The methodology implemented in this package is based on the work of 'Afendras', 'Markatou', and 'Papantonis' (2025) <doi:10.1016/j.jmva.2025.105589>. |
| Depends: | R (≥ 4.0.0) |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| NeedsCompilation: | no |
| Packaged: | 2026-02-05 07:16:49 UTC; nikospapantonis |
| Author: | Nikos Papantonis [aut, cre], Georgios Afendras [aut], Marianthi Markatou [aut] |
| Maintainer: | Nikos Papantonis <feipapantonis@yahoo.gr> |
| Repository: | CRAN |
| Date/Publication: | 2026-02-09 12:00:02 UTC |
Calculate the AUK Estimator
Description
Computes the Area Under the Kendall (AUK) estimator for multivariate independence. The AUK estimator is based on the survival copula and quantifies the deviation from the null hypothesis of independence.
Usage
AUKtest(data)
Arguments
data |
A matrix or data frame of observations where columns represent variables. Must contain at least 2 observations and 2 variables, with no missing values. |
Details
The AUK estimator utilizes the empirical distribution function F_n and a
generalized function g(t) to quantify independence in d dimensions.
Under the null hypothesis of independence, the AUK value tends toward 0.5.
The implementation includes numerical stability fixes for high-dimensional data.
Value
A numeric value in the interval [0, 1] representing the AUK estimator.
References
Afendras, G., Markatou, M., & Papantonis, N. (2025). AUK-based test for mutual independence and an index of mutual dependence. Journal of Multivariate Analysis, 105589. <doi:10.1016/j.jmva.2025.105589>
Examples
# Example 1: Independent Data
set.seed(123)
data_indep <- matrix(runif(300), 100, 3)
AUKtest(data_indep)
# Example 2: Dependent Data
x <- runif(100)
data_dep <- cbind(x, x^2, sqrt(x))
AUKtest(data_dep)