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Maximal Inequalities for Separately Exchangeable Empirical Processes

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  • Harold D. Chiang

Abstract

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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  • Harold D. Chiang, 2025. "Maximal Inequalities for Separately Exchangeable Empirical Processes," Papers 2502.11432, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2502.11432
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    References listed on IDEAS

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    1. Tetsuya Kaji & Elena Manresa & Guillaume Pouliot, 2023. "An Adversarial Approach to Structural Estimation," Econometrica, Econometric Society, vol. 91(6), pages 2041-2063, November.
    2. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    3. A. Belloni & V. Chernozhukov & K. Kato, 2015. "Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems," Biometrika, Biometrika Trust, vol. 102(1), pages 77-94.
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