arXiv 17 Feb 2025 · Econometrics
arXiv:2502.11432 · PDF · DOI · OpenAlex · Extracted main text
This paper derives new maximal inequalities for empirical processes associated with separately exchangeable random arrays. For fixed index dimension $K\ge 1$, we establish a global maximal inequality bounding the $q$-th moment ($q\in[1,\infty)$) of the supremum of these processes. We also obtain a refined local maximal inequality controlling the first absolute moment of the supremum. Both results are proved for a general pointwise measurable function class. Our approach uses a new technique partitioning the index set into transversal groups, decoupling dependencies and enabling more sophisticated higher moment bounds.
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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 | Chiang, H. D., K. Kato, and Y. Sasaki (2023) Inference for high-dimensional exchangeable arrays self | 0.961 | 9 | 3 | 89% |
| 2 | Chen, X. and K. Kato (2019) Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications | 0.928 | 5 | 3 | 80% |
| 3 | de la Peña, V. and E. Giné (1999) Decoupling: From Dependence to Independence | 0.811 | 4 | 2 | 100% |
| 4 | van der Vaart, A. and J. A. Wellner (2011) A local maximal inequality under uniform entropy | 0.737 | 3 | 3 | 67% |
| 5 | Giné, E. and R. Nickl (2016) Mathematical foundations of infinite-dimensional statistical models | 0.644 | 2 | 2 | 100% |
| 6 | van der Vaart, A. W. and J. A. Wellner (1996) Weak Convergence and Empirical Processes | 0.644 | 2 | 2 | 100% |
| 7 | Chernozhukov, V., D. Chetverikov, and K. Kato (2014) Gaussian approximation of suprema of empirical processes | 0.511 | 3 | 2 | 33% |
| 8 | Davezies, L., X. D’Haultfuille, and Y. Guyonvarch (2021) Empirical process results for exchangeable arrays | 0.511 | 2 | 1 | 100% |
| 9 | Chen, X (2018) Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications | 0.405 | 1 | 1 | 100% |
| 10 | Belloni, A., V. Chernozhukov, and K. Kato (2015) Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.