Some deviation inequalities for sums of negatively associated random variables

Abstract

Let $\{X_i,i\ge 1\}$ be a sequence of negatively associated random variables, and let $\{X_i^{\ast },i\ge 1\}$ 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 $k\ge 1$. The well-known results of Shao \cite{Shao2000} sates that $\mathbb{E}f(S_n)\le \mathbb{E}f(S_n^{\ast })$ for any nondecreasing convex function. Using this very strong property, we obtain a large variety of deviation inequalities for $S_n$

References in corpus (1)

• Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment