On bounds for convergence rates in combinatorial strong limit theorems and its applications
DOI:
https://doi.org/10.21638/spbu01.2020.410Abstract
We find necessary and sufficient conditions for convergences of series of weighted probabilities of large deviations for combinatorial sums i Xniπn(i), where Xnij is a matrix of order n of independent random variables and (πn(1), πn(2), . . . , πn(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2, . . . , n, independent with Xnij. We obtain combinatorial variants of results on convergence rates in the strong law of large numbers and the law of the iterated logarithm under conditions closed to optimal ones. We discuss applications to rank statistics.Keywords:
combinatorial sums, convergence rate, law of the iterated logarithm, strong law of large numbers, Baum — Katz bounds, combinatorial strong law of large numbers, combinatorial law of the iterated logarithm, rank statistics, Spearman’s coefficient of rank correlation
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References
Литература
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References
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16. Frolov A. N., “On a combinatorial strong law of large numbers”, Istatistik: Journ. of Turkish Statist. Assoc. 11 (3), 46–52 (2018). Available at: http://jtsa.ieu.edu.tr/current/1.pdf (accessed: September 3, 2020).
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Published
2020-12-27
How to Cite
Frolov, A. N. (2020). On bounds for convergence rates in combinatorial strong limit theorems and its applications. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(4), 688–698. https://doi.org/10.21638/spbu01.2020.410
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
