Test statistic based on the maximum of Chatterjee's rank correlations

This function returns the statistic $$\hat{T}=\sqrt{n}\max_{1\le j\le p}\hat{\xi}_j$$, where \(\hat{\xi}_j\) is the Chatterjee's rank correlation coefficient for the \(j\)-th hypothesis. See Olivares, Olma, and Wilhelm (2025) for details.

Usage

max_stat(dat)

Arguments

dat

List with two elements: vector X and matrix Y. The \(j\)-th column in \(Y\) corresponds to \(Y_j\) in the individual hypothesis \(Y_j \perp X\).

Value

Returns the test statistic.

References

Olivares, M., Olma, T., and Wilhelm, D. (2025). A Powerful Bootstrap Test of Independence in High Dimensions. Preprint, arXiv:2503.21715.

Author

Maurcio Olivares

Tomasz Olma

Daniel Wilhelm