Holger Dette, Fang Han
arXiv 18 Oct 2026 · Mathematics — Statistics Theory
arXiv:2610.25421 · PDF · Extracted main text
Measures of functional dependence that characterize both independence and perfect dependence have attracted growing interest. Despite their appealing theoretical properties, existing rank- and graph-based estimators can suffer from substantial bias under general dependence, limiting their usefulness for statistical inference. Moreover, a systematic and practically accessible framework for mitigating such bias while achieving semiparametric efficiency remains largely unavailable. In this paper, we develop a general framework for efficient estimation of measures of functional dependence through sample-splitting and cross-fitting. Our approach enables systematic bias reduction and semiparametrically efficient inference, and thus offers a flexible and theoretically grounded alternative to existing rank- and graph-based methods.
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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 | Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Du… (2018) Double/debiased machine learning for treatment and structural parameters | 1.000 | 5 | 4 | 100% |
| 2 | Chatterjee, Sourav (2021) A new coefficient of correlation | 1.000 | 5 | 3 | 100% |
| 3 | Gao, Muhong and Han, Fang and Li, Qizhai (2026) Limit theorems of Azadkia-Chatterjee's conditional graph correlation self | 0.928 | 4 | 3 | 100% |
| 4 | Klein, Thierry and Lagnoux, Agnès and Rochet, Paul and Nguyen, Thi M… (2026) Asymptotic efficiency for Sobol' and Cramér-von Mises indices under two designs of experiments | 0.928 | 4 | 3 | 100% |
| 5 | Newey, Whitney K and Robins, James R (2018) Cross-fitting and fast remainder rates for semiparametric estimation | 0.843 | 3 | 3 | 100% |
| 6 | Shi, H and Drton, M and Han, F (2022) On the power of Chatterjee's rank correlation self | 0.843 | 3 | 3 | 100% |
| 7 | Dette, Holger and Siburg, Karl F. and Stoimenov, Pavel A (2013) A copula-based non-parametric measure of regression dependence self | 0.811 | 4 | 2 | 100% |
| 8 | Chhaibi, Reda and Gamboa, Fabrice and Pellegrini, Clément (2026) A martingale approach to fluctuations of rank estimators in sensitivity analysis | 0.811 | 4 | 2 | 100% |
| 9 | Ansari, Jonathan and Fuchs, Sebastian (2025) An ordering for the strength of functional dependence | 0.737 | 3 | 2 | 100% |
| 10 | Ansari, Jonathan and Langthaler, Patrick B and Fuchs, Sebastian and… (2026) Quantifying and estimating dependence via sensitivity of conditional distributions | 0.737 | 3 | 2 | 100% |
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