# Some deviation inequalities for sums of negatively associated random variables

@article{Zhang2020SomeDI, title={Some deviation inequalities for sums of negatively associated random variables}, author={Wencong Zhang}, journal={arXiv: Probability}, year={2020} }

Let $\{X_i,i\geq1\}$ be a sequence of negatively associated random variables, and let $\{X_i^\ast,i\geq 1\}$ be a sequence of independent random variables such that $X_i^\ast$ and $X_i$ have the same distribution for each $i$. Denote by $S_k=\sum_{i=1}^{k}X_i$ and $S_k^\ast=\sum_{i=1}^{k}X_i^\ast$ for $k\geq 1$. The well-known results of Shao \cite{Shao2000} sates that $\mathbb{E}f(S_n)\leq \mathbb{E}f(S_n^\ast)$ for any nondecreasing convex function. Using this very strong property, we obtain…

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