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

Debapratim Banerjee, Matteo Sordello

We consider the three dimensional array $\mathcal{A}=\{a_{i,j,k}{\}}_{1\le i,j,k\le n}$, with $a_{i,j,k}\in [0,1]$, and the two random statistics $T_{1}:= \sum_{i=1}^n \sum_{j=1}…