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Quick and Complete Convergence in the Law of Large Numbers with Applications to Statistics
Version 1
: Received: 11 May 2023 / Approved: 12 May 2023 / Online: 12 May 2023 (08:25:35 CEST)
A peer-reviewed article of this Preprint also exists.
Tartakovsky, A.G. Quick and Complete Convergence in the Law of Large Numbers with Applications to Statistics. Mathematics 2023, 11, 2687. Tartakovsky, A.G. Quick and Complete Convergence in the Law of Large Numbers with Applications to Statistics. Mathematics 2023, 11, 2687.
Abstract
In the first part of this article, we discuss and generalize the complete convergence introduced by Hsu and Robbins (1947) to the r-complete convergence introduced by Tartakovsky (1998). We also establish its relation to the r-quick convergence first introduced by Strassen (1967) and extensively studied by Lai (1976). Our work is motivated by various statistical problems, mostly in sequential analysis. As we show in the second part, generalizing and studying these convergence modes is important not only in probability theory but also to solve challenging statistical problems in hypothesis testing and changepoint detection for general stochastic non-i.i.d. models.
Keywords
Complete convergence; r-quick convergence; sequential analysis; hypothesis testing; changepoint detection
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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