A Bernstein type inequality for sums of selections from three dimensional arrays

Debapratim Banerjee and Matteo Sordello

Statistics & Probability Letters, 2019, vol. 154, issue C, -

Abstract: We consider the three dimensional array A={ai,j,k}1≤i,j,k≤n, with ai,j,k∈[0,1], and the two random statistics T1≔∑i=1n∑j=1nai,j,σ(i) and T2≔∑i=1nai,σ(i),π(i), where σ and π are chosen independently from the set of permutations of {1,2,…,n}. These can be viewed as natural three dimensional generalizations of the statistic T3=∑i=1nai,σ(i), considered by Hoeffding (1951). Here we give Bernstein type concentration inequalities for T1 and T2 by extending the argument for concentration of T3 by Chatterjee (2005).

Keywords: Concentration inequalities; Method of exchangeable pairs; Permutations (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.06.010

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