Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains

Lê Thành ()
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Lê Thành: Vinh University

Statistical Papers, 2024, vol. 65, issue 3, No 1, 1135-1162

Abstract: Abstract This paper provides sets of sufficient conditions for mean convergence theorems for arrays of dependent random variables. We expand and improve a number of particular cases in the literature including Theorem 2.1 in Sung (Appl Math Lett 26(1):18–24, 2013), Theorems 3.1–3.3 in Wu and Guan (J Math Anal Appl 377(2):613–623, 2011), and Theorem 3 in Lita da Silva (Results Math 74(1):1–11, 2019), among others. The proof is different from those in the aforementioned papers and the main results can be applied to obtain mean convergence results for arrays of functions of non-homogeneous Markov chains and dependent bootstrap.

Keywords: Mean convergence; Weak law of large numbers; Negative dependence; Non-homogeneous Markov chain; Dependent bootstrap; 60F05; 60F25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01427-y

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