Performs a distance correlation t-test of multivariate independence, based on the distance correlation t-statistic introduced by Székely and Rizzo (2013). This implementation executes the statistical approach of energy::dcorT.test, but is written in C++ for improved performance. The function supports testing for dependence between multivariate random vectors and uses a t-distribution approximation under the null hypothesis of independence. Empirical benchmarks indicate that this C++ version can be significantly faster than the original R version in the energy package, especially for larger sample sizes (e.g., 1.5–3x faster for n = 10,000).
Value
[list]
returns a list containing:
- method
description of test.
- statistic
observed value of the test statistic.
- parameter
degrees of freedom.
- estimate
bias corrected squared measure of distance correlation between x and y.
- p.value
p-value of the t-test.
- data.name
description of data.
References
Székely, G. J., & Rizzo, M. L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, 117, 193–213. URL: https://doi.org/10.1016/j.jmva.2013.02.012. Székely, G. J., & Rizzo, M. L. (2014). Energy statistics: A class of statistics based on distances. Journal of Statistical Planning and Inference, 143(8), 1249–1272. URL: https://doi.org/10.1016/j.jspi.2013.03.018.
Examples
dcor_t_test(iris[, "Petal.Length"], iris[, c("Sepal.Length", "Sepal.Width")])
#> $statistic
#> [1] 132.974
#>
#> $parameter
#> [1] 11024
#>
#> $p.value
#> [1] 0
#>
#> $estimate
#> [1] 0.7848375
#>
#> $method
#> [1] "dcor t-test of independence for high dimension"
#>
#> $data.name
#> [1] "x and y"
#>