Published July 4, 2023
| Version v1
Publication
Moment inequalities for sums of weakly dependent random fields
Contributors
Others:
- Laboratoire de Mathématiques d'Orsay (LMO) ; Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
- Understanding the Shape of Data (DATASHAPE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)
- Institut für Mathematik [Potsdam] ; University of Potsdam = Universität Potsdam
- Department of Mathematics [Munich] ; Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM)
- DFG Forschungsgruppe FOR 5381 "Mathematical Statistics in the Information Age - Statistical Efficiency and Computational Tractability"
- DFG CRC 1294 - 318763901 'Data Assimilation'
- Emmy Noether grant MuSyAD (CA 1488/1-1)
- ANR-19-CHIA-0021,BISCOTTE,Approches statistiquement et computationnellement efficicaces pour l'intelligence artificielle(2019)
- ANR-21-CE23-0035,ASCAI,Segmentation, clustering, et seriation actifs et passifs: vers des fondations unifiées en IA(2021)
Description
We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums over a rectangulargrid of dimension $d$ of a random field satisfying a weak dependency assumption of projective type:the difference between the expectation of an element of the random field and its conditional expectationgiven the rest of the field at a distance more than $\delta$ is bounded, in $L^p$distance, by a known decreasing function of $\delta$. The analysis is based on the combination of a multi-scale approximation of random sums by martingale difference sequences, andof a careful decomposition of the domain. The obtained results extend previously known bounds under comparable hypotheses, and do not use the assumption of commuting filtrations.
Additional details
Identifiers
- URL
- https://hal.science/hal-04150509
- URN
- urn:oai:HAL:hal-04150509v1
Origin repository
- Origin repository
- UNICA