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Title: Berry-Esseen bounds for functionals of independent random variables
Authors: Privault, Nicolas
Serafin, Grzegorz
Keywords: Science::Mathematics
Issue Date: 2022
Source: Privault, N. & Serafin, G. (2022). Berry-Esseen bounds for functionals of independent random variables. Electronic Journal of Probability, 27.
Journal: Electronic Journal of Probability
Abstract: We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on a continuous-time integration by parts setting and discrete chaos expansions methods. Our approach improves on related results obtained in discrete-time integration by parts settings and applies to U-statistics satisfying the weak assumption of decomposability in the Hoeffding sense, and yield Kolmogorov distance bounds instead of the Wasserstein bounds previously derived in the special case of degenerate U-statistics. Linear and quadratic functionals of arbitrary sequences of independent random variables are included as particular cases, with new fourth moment bounds, and applications are given to Hoeffding decompositions, weighted U-statistics, quadratic forms, and random subgraph weighing. In the case of quadratic forms, our results recover and improve the bounds available in the literature, and apply to matrices with non-empty diagonals.
ISSN: 1083-6489
DOI: 10.1214/22-EJP795
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 The Authors. All rights reserved. This paper was published by Bernouli Society and the Institute of Mathematical Statistics in Electronic Journal of Probability and is made available with permission of the authors.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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