arXiv 24 Mar 2023 · Mathematics — Statistics Theory · publishedBiometrika (2024) · 10 citations (OpenAlex)
arXiv:2303.14088 · PDF · DOI · OpenAlex · Extracted main text
While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under an additional independence assumption, and complement our theory with simulation evidence for general settings. Chatterjee's rank correlation thus falls into a category of statistics that are asymptotically normal but bootstrap inconsistent. Valid inferential methods in this case are Chatterjee's original proposal (for testing independence) and Lin and Han (2022)'s analytic asymptotic variance estimator (for more general purposes).
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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 | Lin, Z. and Han, F (2022) Limit theorems of Chatterjee's rank correlation self | 1.000 | 8 | 4 | 100% |
| 2 | Abadie, A. and Imbens, G. W (2008) On the failure of the bootstrap for matching estimators | 0.843 | 3 | 3 | 100% |
| 3 | Bickel, P. J. and Freedman, D. A (1981) Some asymptotic theory for the bootstrap | 0.737 | 3 | 2 | 100% |
| 4 | Chatterjee, S (2021) A new coefficient of correlation | 0.737 | 3 | 2 | 100% |
| 5 | Beran, R (1997) Diagnosing bootstrap success | 0.644 | 2 | 2 | 100% |
| 6 | Drton, M. and Williams, B (2011) Quantifying the failure of bootstrap likelihood ratio tests | 0.644 | 2 | 2 | 100% |
| 7 | Fang, Z. and Santos, A (2019) Inference on directionally differentiable functions | 0.644 | 2 | 2 | 100% |
| 8 | Samworth, R (2003) A note on methods of restoring consistency to the bootstrap | 0.644 | 2 | 2 | 100% |
| 9 | Arcones, M. A. and Gine, E (1992) On the bootstrap of U and V statistics | 0.511 | 2 | 1 | 100% |
| 10 | Bickel, P. J (2022) Measures of independence and functional dependence | 0.511 | 2 | 1 | 100% |
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