Laurent Davezies, Xavier D'Haultfoeuille, Yannick Guyonvarch
arXiv 24 Jun 2019 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2021) · 7 citations (OpenAlex)
arXiv:1906.11293 · PDF · DOI · OpenAlex · Extracted main text
Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same population. Examples include trade flows between countries or relationships in a network. Separately exchangeable arrays are well suited to multiway clustering, where units sharing the same cluster (e.g. geographical areas or sectors of activity when considering individual wages) may be dependent in an unrestricted way. We prove uniform laws of large numbers and central limit theorems for such exchangeable arrays. We obtain these results under the same moment restrictions and conditions on the class of functions as those typically assumed with i.i.d. data. We also show the convergence of bootstrap processes adapted to such arrays.
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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 | Menzel (2019) Bootstrap with cluster-dependence in two or more dimensions | 1.000 | 6 | 3 | 100% |
| 2 | van der Vaart (2000) Asymptotics Statistics, Cambridge University Press | 1.000 | 5 | 3 | 100% |
| 3 | van der Vaart \ Wellner (1996) Weak Convergence of Empirical Processes: with Applications to Statistics, Springer-Verlag New York | 0.965 | 10 | 3 | 90% |
| 4 | Santos Silva \ Tenreyro (2006) `The log of gravity', The Review of Economics and statistics 88(4), 641–658 | 0.874 | 9 | 2 | 100% |
| 5 | Giné \ Nickl (2015) Mathematical Foundations of Infinite-Dimensional Statistical Models, Cambridge Series in Statistical and Probabilistic Mathemati… | 0.843 | 4 | 3 | 75% |
| 6 | McCullagh (2000) `Resampling and exchangeable arrays', Bernoulli 6(2), 285–301 | 0.843 | 3 | 3 | 100% |
| 7 | Owen (2007) `The pigeonhole bootstrap', The Annals of Applied Statistics 1(2), 386–411 | 0.843 | 3 | 3 | 100% |
| 8 | de la Peña \ Giné (1999) Decoupling | 0.737 | 3 | 3 | 67% |
| 9 | Aldous (1981) `Representations for partially exchangeable arrays of random variables', Journal of Multivariate Analysis 11(4), pp | 0.644 | 2 | 2 | 100% |
| 10 | Eagleson \ Weber (1978) `Limit theorems for weakly exchangeable arrays', Mathematical Proceedings of the Cambridge Philosophical Society 84(1), 123–130 | 0.644 | 2 | 2 | 100% |
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