The paper proves the Strong Law of Large Numbers for integral functionals of random fields with unboundedly increasing covariances. The case of functional data and increasing domain asymptotics is studied. Conditions to guarantee that the Strong Law of Large Numbers holds true are provided. The considered scenarios include wide classes of non stationary random fields. The discussion about application to weak and long-range dependent random fields and numerical examples are given.
This research was supported under La Trobe University SEMS CaRE Grant"Asymptotic analysis for point and interval estimation in some statistical models". The research of the last listed author was partially funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project 1.13556.2019/13.1.
JournalCommunications in Statistics: Theory and Methods
PublisherTaylor & Francis
Rights StatementThis is an Accepted Manuscript version of the following article, accepted for publication in Communications in Statistics: Theory and Methods. Illia Donhauzer, Andriy Olenko & Andrei Volodin (2022) Strong law of large numbers for functionals of random fields with unboundedly increasing covariances, Communications in Statistics - Theory and Methods, 51:20, 6947-6962, DOI: 10.1080/03610926.2020.1868515. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.