Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains (Q6579370)
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scientific article; zbMATH DE number 7887479
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains |
scientific article; zbMATH DE number 7887479 |
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Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains (English)
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25 July 2024
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The author establishes a weak law of large numbers (giving convergence in probability) and a mean convergence theorem (giving convergence in \(\mathcal{L}_p\) for some \(1\leq p<2\)) for arrays of random variables satisfying a dependence condition that includes pairwise negative dependence, extended negative dependence, \(m\)-dependence, wide orthant dependence, and functions of non-homogeneous Markov chains as special cases. These results unify and extend several results from the literature. Extensive discussion is given of several special cases and applications, including the case where certain dominating coefficients are uniformly bounded, wide orthant dependence, functions of non-homogeneous Markov chains, and a dependent bootstrap.
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mean convergence
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weak law of large numbers
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negative dependence
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non-homogeneous Markov chain
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dependent bootstrap
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