Mauricio Olivares, Tomasz Olma, Daniel Wilhelm
arXiv 27 Mar 2025 · Statistics — Methodology
arXiv:2503.21715 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a nonparametric test of pairwise independence of one random variable from a large pool of other random variables. The test statistic is the maximum of several Chatterjee's rank correlations and critical values are computed via a block multiplier bootstrap. The test is shown to asymptotically control size uniformly over a large class of data-generating processes, even when the number of variables is much larger than sample size. The test is consistent against any fixed alternative. It can be combined with a stepwise procedure for selecting those variables from the pool that violate independence, while controlling the family-wise error rate. All formal results leave the dependence among variables in the pool completely unrestricted. In simulations, we find that our test is very powerful, outperforming existing tests in most scenarios considered, particularly in high dimensions and/or when the variables in the pool are dependent.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chatterjee, Sourav (2021) A new coefficient of correlation | 0.965 | 10 | 4 | 90% |
| 2 | Zhou, Yeqing and Xu, Kai and Zhu, Liping and Li, Runze (2024) Rank-based indices for testing independence between two high-dimensional vectors | 0.874 | 6 | 2 | 100% |
| 3 | Székely, Gábor J. and Rizzo, Maria L. and Bakirov, Nail K (2007) Measuring and testing dependence by correlation of distances | 0.874 | 5 | 2 | 100% |
| 4 | Székely, Gábor J. and Rizzo, Maria L (2013) The distance correlation t-test of independence in high dimension | 0.811 | 4 | 2 | 100% |
| 5 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors | 0.737 | 4 | 3 | 50% |
| 6 | Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2019) Inference on causal and structural parameters using many moment inequalities | 0.737 | 3 | 3 | 67% |
| 7 | Zhu, Changbo and Zhang, Xianyang and Yao, Shun and Shao, Xiaofeng (2020) Distance-based and RKHS-based dependence metrics in high dimension | 0.737 | 3 | 2 | 100% |
| 8 | Lin, Z and Han, F (2022) On boosting the power of Chatterjee's rank correlation | 0.644 | 2 | 2 | 100% |
| 9 | Lin, Zhexiao and Han, Fang (2024) On the failure of the bootstrap for Chatterjee's rank correlation | 0.644 | 2 | 2 | 100% |
| 10 | Shi, H and Drton, M and Han, F (2021) On the power of Chatterjee's rank correlation | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bias correction for Chatterjee's graph-based correlation coefficient | 0.405 | 1 | 1 |
| 2 | Limit theorems of Azadkia-Chatterjee's conditional graph correlation | 0.405 | 1 | 1 |