ON A COMBINATORIAL STRONG LAW OF LARGE NUMBERS

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Türkiye İstatistik Derneği Dergisi
Volume:11 Issue:3
ON A COMBINATORIAL STRONG LAW OF LARGE NUMBERS

ON A COMBINATORIAL STRONG LAW OF LARGE NUMBERS

Authors : Andrei N FROLOV

Pages : 46-52

View : 20 | Download : 8

Publication Date : 2018-12-31

Article Type : Research Paper

Abstract :We derive strong laws of large numbers for combinatorial sums iXniπninsert ignore into journalissuearticles values(i);, where Xnij are n × n matrices of random variables with finite fourth moments and insert ignore into journalissuearticles values(πninsert ignore into journalissuearticles values(1);, . . . , πninsert ignore into journalissuearticles values(n);); are uniformly distributed random permutations of 1, . . . , n independent with X’s. We do not assume the independence of X’s, but this case is included as well. Examples are discussed.
Keywords : Combinatorial central limit theorem, combinatorial sums, strong law of large numbers

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